Math 2

Question 0

Simplify the fraction:
4 14 5
—- x —- x —-
21 13 8

Answer 0

Prime numbers and cancellation (numerators with denominators) is a convenient approach.
2 x 2 x 2 x 7 x 5 5
———————– = —-
3 x 7 x 13 x 2 x 2 x 2 39

Question 1

Simplify the Fraction
6x
—-
70

Answer 1

35

Question 2

To evaluate 6.75 x 10^3:

Answer 2

Move the decimal to the right 3 places.

6,750.

Question 3

To evaluate 72.12 x 10^-4:

Answer 3

Move the decimal to the left 4 places.

0.007212

Question 4

To evaluate 54.197 / 10^2:

Answer 4

Because we are dividing by 10^2, we move the decimal to the left 2 places.

Question 5

Convert 70% as a Fraction and Decimal:

Answer 5

Fraction:
7
—
10

Decimal
0.7

Question 6

Convert 100% as Fraction and Decimal:

Answer 6

Fraction:
1
Decimal
1.0

Question 7

Sometimes it is convenient to rewrite a fraction in order to separate a variable.
For example, three quarters of “T”.
3T
—-
4
How could be the other form of the fraction?

Answer 7

3
— T
4

Question 8

How many zeros are there in a Billion?

Answer 8

9.

17 Billion = 17,000,000,000

Question 9

In the question, “How many one-fourths are in 3/5 of 25/2”, where does the variable goes?

Answer 9

x 3 25
—- = — X —
4 5 2

x = 30

Question 10

Multiplier of 7.5% increase?

Answer 10

1.075

Question 11

Multiplier of a reduction of 8.8%?

Answer 11

1 - 0.088 = 0.912

Question 12

In a percent difference problem, when involved decimals (those squared get smaller), I have to perform the subtraction in order of appearance of the quantities.

Answer 12

After, I have to divide by the basis of the comparison, which is what follows the word “than”, in the problem statements.

Question 13

In a percent difference problem, when involved decimals (which squared get smaller), I have to perform the subtraction in order of appearance of the quantities.

Answer 13

After, I have to divide by the basis of the comparison, which is what follows the word “than”, in the problem statements.

Question 14

Can I reduce terms to simplify the math when multiplying fractions?

Answer 14

Yes.
3/8 x 12/5 x 5/2 reduces to:
3/8 x 6/1 x 1/1
It is cross cancelation. The numerator of one fraction can get reduced by the denominator of other fraction.

Question 15

Can I reduce terms to simplify the math when multiplying fractions?

Answer 15

Yes.
3/8 x 12/5 x 5/2 reduces to:
3/8 x 6/1 x 1/1
It is cross cancelation. The numerator of one fraction can get reduced by the denominator of other fraction.

Question 16

x - 4

Answer 16

x + 4

-16 and -4 turns positive +4

Question 17

(2x) (3x) =

Answer 17

6x^2

Never forget to square the variables too.

Question 18

2x^2 + 11 - 6 = 0

Answer 18

I can factor out the 2, and divide 11/2 = 5.5

In this exercises I can also work with decimals.

Question 19

“DISTANCE” FORMULA

Answer 19

(Rate) (Time)

Remember the fraction D/RT, and isolate the variable you need.

Question 20

“RATE” FORMULA

Answer 20

Time
Remember the fraction D/RT, and isolate the variable you need.

Question 21

“TIME” FORMULA

Answer 21

Rate
Remember the fraction D/RT, and isolate the variable you need.

Question 22

On a Distance / Rate / Time problems, remember:

Answer 22

1. If the *cars are moving apart and I have to find the average speed of each *car, I have to pay attention to the “Total Distance Apart from each other” number (given in the problem).
2. Use the proper formula.
3. Then set an equation in which I add up the Distance 1 + Distance 2 = “Total Distance Apart from each other” number (given in the problem).

Question 23

Pythagorean Theorem:

If I know two sides I can get the Hypotenuse. Get it with sides 6 and 7:

Answer 23

(6)^2 + (7)^2 = Square Root of 85
(6)^2 = 36
+
(7)^2 = 49
——
85. -> Then, I just add the Square Root symbol.

Question 24

SLOPE (m) FORMULA

Answer 24

Second x - First x

Question 25

COORDINATE GEOMETRY

How can I get the “y - intercept”?

Answer 25

In the Slope Formula (m): y = mx + b, “b” is the “y - intercept”.

1. Take the “x” and “y” coordinates of the same point. Ex. (3,2)
2. Plug them into the Slop Formula, into the “y” and “x” variables.
3. Plug in the Slope for “m”.
4. Solve for “b”.

Question 26

k(2) + 3k(1) = 17

Answer 26

2k + 3k = 5k = 17 —-> k = 17/5
I arranged the “2” to properly perform the addition.
k(2) = 2k

Question 27

SLOPE is

Answer 27

RUN

Question 28

(-3x)^2 =

x = 2

Answer 28

36.
(-6)^2

Incorrect to square each the -3 and the x. The multiplication inside the parenthesis is first, then I can square.

Question 29

SIMPLIFY

x - (3 - x)

Answer 29

2x - 3

x - 3 + x = 2x - 3

If a negative sign is right to the parenthesis I have to multiply if by the signs inside the parenthesis. That’s why I got the “+x”, resulting in the “2x”.

Question 30

Distributive Law

A (B + C) =

Answer 30

AB + AC
It works with addition and subtraction. 
A (B - C) = AB - AC
It does not work with multiplication:
3(xy) does NOT equal (3x) (3y) ---> It equals 3xy

Question 31

(x^a) (x^b) =

Answer 31

x^a+b

Question 32

Is (a + b)^2 = a^2 + b^2 ?

Answer 32

No.
It is absolutely illegal to “distribute” an exponent across addition and subtraction.
Instead we use the square of a sum.

Question 33

Explain this algebraic pattern:

a^2 - b^2

Answer 33

This pattern is known as the Difference of Two Squares.

a^2 - b^2 = (a + b) (a - b)

Question 34

Elaborate the expression:

9x^2 - 16

Answer 34

See the pattern. It is a Difference of Two Squares.

3x - 4) (3x + 4

Question 35

Difference of Two Squares

x^7 - 4x^5 =

Answer 35

x^5 (x^2 - 4) = x^5 (x + 2) (x - 2)

Question 36

Remember that The Difference of Two Squares cannot be that obvious.
y^2 = x^2 + k

Answer 36

Then, “k” = y^2 - x^2 = (x + y) (x - y)

Question 37

When Algebraically asked to find the side of a geometric figure, such as a Square, I might get two results of “x” (which is the side). One positive and one negative. So I have to pick…

Answer 37

The positive number. I have to discard the negative value.

The edge of a square must be positive.

Question 38

In the “Which Quantity is Greater A or B”, GRE exercises, what are the options?

Answer 38

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.

Question 39

INEQUALITIES

When finding possible values of “x”, and I have been given two expressions, one way to get them is:

Answer 39

To align the expressions and add them up.
One variable must cancel out.
I have to solve for the desired variable.
Turn the sign if I’m dividing by a negative number.

Question 40

INEQUALITY
|2x - 4| < 6
When solving for an absolute value of “x”, I have to:

Answer 40

Divide the inequality into two parts:
2x-4 < 6                 2x-4 > -6
Solve each one.
Finally, you will get a range in which "x" will be located.
Express it in one range. 
-1 < "x" < 5

Question 41

GEOMETRY
Acute Angles?
Ángulos Agudos

Answer 41

Miden menos de 90 grados.

Question 42

GEOMETRY
Obtuse Angles
Ángulos Obtusos

Answer 42

Miden más de 90 grados.

Question 43

GEOMETRY

3-D Formula to get the Volume of a Cube:

Answer 43

S^3

*S = Side

Question 44

GEOMETRY

3-D Formula to get the Surface Area of a Cube:

Answer 44

6s^2

Question 45

What does “This year the GRE All Stars had 3 times as many wins, and one-half as many losses as they had last year”, means?

Answer 45

2014 2015
Wins X 3X
Losses Y Y/2

Question 46

Is 2sb = 2s * 2b ?

Answer 46

No.

2s * 2b = 4sb

Question 47

Usually, how does a Function looks like in a graph? How can I identify the graph?
For example: g (x) = |x-1| -1

Answer 47

The function is an absolute value, which typically has a V-shape.
I can identify the correct graph by trying x = 0, which yields g (0) = 0, the origin.
Then, try x = 1, which yields g (1) = -1. And the point (0,-1).
I can try with some other numbers and see where they fall on a graph.

Question 48

-3(-2) + 6/3 - (-5) =

Answer 48

13

6 + 2 + 5 = 13

Question 49

-5^2

Answer 49

-25

Make sure to read this as -(5^2); NOT, (-5)^2 = 25

Question 50

3 x 99 - 2 x 99 - 1 x 99 =

Answer 50

0
99 (3 - 2 - 1) =
99 (0) = 0

Question 51

Can I solve a couple of equal equations to get the value of two variables?

Answer 51

No.
There would be the same equations.
I can only solve two equations for two variables if the equations are different.

Question 52

GEOMETRY

Punto donde dos líneas se encuentran:

Answer 52

Vértice - Vertex

Question 53

GEOMETRY

Acute Angles - Ángulos Agudos miden menos de:

Answer 53

90 grados

Question 54

GEOMETRY

Ángulos Rectos - Right Angles, miden exactamente:

Answer 54

90 grados

Question 55

GEOMETRY

Straight Angles - Ángulos Llanos, miden exactamente:

Answer 55

180 grados

Question 56

GEOMETRY

Define “Complementary Angles”

Answer 56

Ángulos Complementarios.

Cuando la medida de dos ánguulos suma 90 grados

Question 57

GEOMETRY

Define “Supplementary Angles”

Answer 57

Ángulos Suplementarios

Cuando la medida de dos ángulos suma 180 grados

Question 58

GEOMETRY

Define “Perpendicular Lines”

Answer 58

Dos líneas que se encuentran en “ángulo recto” son perpendiculares.
Si te dicen que dos líneas son perpendiculares, piensa 90 grados.

Question 59

GEOMETRY

Define “Polygons”

Answer 59

Un Polígono es una figura de dos dimensiones con tres o más lados rectos; llamados de acuerdo al número de lados que tengan.

3 - Triangle
4 - Quadrilateral
5 - Pentagon

Question 60

GEOMETRY

¿Cómo calculo la suma de los ángulos interiores de un “Polygon”?

Answer 60

Suma de los ángulos interiores en un Polígono de “n” lados = (n-2)180

Question 61

GEOMETRY

¿Cuál es la suma de los ángulos exteriores de cualquier Polígono?

Answer 61

360 grados.

Question 62

GEOMETRY

En un Triángulo, la medida del ángulo exterior es igual a:

Answer 62

La suma de los ángulos remotos interiores.

Si tengo el Triángulo A,B,C, el ángulo fuera y hacia la derecha de “C” es A + B

Question 63

GEOMETRY

Define “Isosceles Triangles”

Answer 63

1. Los Triángulos Isósceles tienen dos lados iguales y dos ángulos iguales.
2. Los dos ángulos iguales están opuestos a los dos lados iguales.
3. Si sé que es un Triángulo Isósceles, con saber cuánto mide uno de sus ángulos, puedo calcular la medida de los otros dos.

Question 64

GEOMETRY

Si un Triángulo tiene dos lados que miden lo mismo (y por ende, dos ángulos que miden lo mismo), sé que se trata de:

Answer 64

Un Triángulo Isósceles.

Question 65

GEOMETRY

Define “Equilateral Triangles”

Answer 65

1. Tienen tres lados iguales y tres ángulos iguales.

2. Como 180 grados entre 3 = 60, cada uno de sus tres ángulos interiores mide 60 grados.

Question 66

GEOMETRY

Define “Right Triangles”

Answer 66

1. Es cualquier triángulo con un ángulo de 90 grados.
2. El lado opuesto al ángulo recto: Hipotenusa
3. Tienen su propia regla: Pythagorean Theorem ->
   a^2 + b^2 = c^2

Question 67

GEOMETRY

Define “Special Right Triangles”

Answer 67

Dos Triángulos Rectos que con frecuencia aparecen en el exámen:
30-60-90 y 45-45-90

Question 68

GEOMETRY

Características del “Special Right Triangle”, 30-60-90.

Answer 68

Leg : Leg : Hypotenuse
x x * Square Root of Three 2x

Hidden in “Equilateral Triangles”

Question 69

GEOMETRY

Define “Equilateral Triangles”

Answer 69

1. Tienen tres lados iguales y tres ángulos iguales.

2. Como 180 grados entre 3 = 60, cada uno de sus tres ángulos interiores mide 60 grados.

Question 70

GEOMETRY

Características del “Special Right Triangle”, 30-60-90.

Answer 70

Leg : Leg : Hypotenuse
x x * Square Root of Three 2x

Hidden in “Equilateral Triangles”

Question 71

GEOMETRY

Define “Special Right Triangle”, 45-45-90

Answer 71

También llamado: “Isosceles Right Triangle”.
Leg : Leg : Hypotenuse
x x x * Square Root of 2

Hidden in Squares

Question 72

GEOMETRY

Define “Congruent Triangles”

Answer 72

Triángulos que tienen misma forma y tamaño. Son idénticos, pero tienen diferente orientación en el espacio.

Question 73

GEOMETRY

Define “Similar Triangles”

Answer 73

Dos Triángulos son Similares si sus tres ángulos son idénticos.
Tienes la misma forma pero no necesariamente el mismo tamaño.
Probable pregunta GRE: Determinar cuál es el grado en el que un Triángulo es mayor que otro.
La relación (Ratio), de cualquier par de lados es la misma.
a b c
– = – = –
X Y Z

Question 74

GEOMETRY

Define “Quadrilaterals”

Answer 74

1. Polígono de 4 lados.
2. Sus 4 ángulos internos suman 360 grados.
3. Cinco tipos principales: Square, Rectangle, Parallelogram, Trapezoid, Rhombus.

Question 75

GEOMETRY

Define “Parallelograms”

Answer 75

Un Paralelogramo es un Cuadrilátero.

Area = b x h

Question 76

GEOMETRY

Define “Diagonals of a Rectangle”

Answer 76

La diagonal de un Rectángulo forma Triángulos Rectos que incluyen la diagonal y dos lados del rectángulo.
Si conoces dos de estos valores, puedes calcular el tercero con el Teorema de Pitágoras.

Question 77

GEOMETRY

Define “Diagonals of a Square”

Answer 77

Una diagonal divide al cuadrado en dos “Special Right Triangles”, 45-45-90
Dos diagonales, dividen al Cuadrado en cuatro triángulos 45-45-90

Question 78

GEOMETRY

Circumference of a Circle formula:

Answer 78

2 * PI * r
O bien:
c = PI * d

Question 79

GEOMETRY

Podemos calcular la longitud del Arco de un Círculo, si conocemos:

Answer 79

1. Radio
2. La medida del ángulo central (ángulo cuyo vértice es el centro del Círculo), del inscrito (ángulo cuyo vértice se encuentra sobre la circunferencia del círculo), que forman el Arco.
   Formula: Arc Length = n/360 x 2PIr
   “n” es la medida en grados del Arco.

Question 80

GEOMETRY

Define “Area of a Sector”

Answer 80

Un “Sector” es una “rebanada de pizza”.

n/360 * PI r^2

Question 81

GEOMETRY

Define “Concentric Circles”

Answer 81

Dos o más círculos con el mismo centro

Question 82

GEOMETRY

What does it mean: “Circle A is perfectly inscribed in a Square; and the Square is perfectly inscribed within Circle B?

Answer 82

1. Circulo A, dentro del Cuadrado.

2. Cuadrado dentro del Círculo B.

Question 83

WORD PROBLEMS

What it means: 8 more than “x”

Answer 83

x + 8

Question 84

WORD PROBLEMS

What it means: “x less than 2”

Answer 84

2 - x

Question 85

WORD PROBLEMS

What it means: “2 less 16”

Answer 85

2 - 16

Question 86

WORD PROBLEMS

What it means: “y can take any value up to 4”

Answer 86

y <_ 4 Four or less

Question 87

WORD PROBLEMS

What it means: “y has a value of at least 4”

Answer 87

y _> 4 4 or more

Question 88

WORD PROBLEMS

What it means: “The quotient of a and b”

Answer 88

a/b

Question 89

WORD PROBLEMS

What it means: “One-Third the difference of a and b”

Answer 89

(1/3) (a-b)

Question 90

WORD PROBLEMS

What it means: “a seven times itself”

Answer 90

a^7

Question 91

WORD PROBLEMS

What it means: “A is half the size of B”

Answer 91

A = 1/2B

Question 92

WORD PROBLEMS

What it means: “A is 5 less than B”

Answer 92

A = B - 5

Question 93

WORD PROBLEMS

What it means: “Twice as many Girls (G) as Boys (B)”

Answer 93

G = 2B

Question 94

WORD PROBLEMS

What it means: “P is x per cent of Q”

Answer 94

P = x/100 Q

Or:

P/Q = x/100

Question 95

WORD PROBLEMS

What it means: “The Tens digit of a 2-digit number is trice the Units digit”

Answer 95

El valor del número es:
(3x * 10) + (x * 1) = 30x + x = 31x
*10 porque es “decenas” *1 porque son Unidades
Si se invirtieran los dos números, el nuevo número sería 13x

Question 96

How to find the minimum value of the Function f(x) = x^2 + 4x - 5

Answer 96

1. Factor the quadratic = (x+5) (x-1)
2. x = -5, 1
3. A quadratic reaches its extreme value halfway between these solutions, that is: 1+(-5) / 2 = -2
4. Substitute for “x”: f(-2) = 4 + 4(-2) - 5 = -9
   Correct answer: -9

Question 97

Which is the most effective way to combine two inequalities?

Answer 97

To line up the inequality symbols and add both sides. This can only be done if the inequality symbols face in the same direction.
You can “flip” one of the inequalities by multiplying for -1

Question 98

CONJUNTOS Y DIAGRAMAS DE VENN

Formula para relacionar “Dos Grupos”

Answer 98

G1 + G2 - Ambos + Ninguno = Total

Question 99

0!

Answer 99

1

Question 100

How many different anagrams are possible for the word ATLANTA?

Answer 100

3! 2!

*Tenemos múltiples repeticiones: tres A’s y dos T’s

Question 101

COMBINATIONS

En las combinaciones…

Answer 101

El orden no importa.

Question 102

COMBINATIONS

Combination Formula

Answer 102

nCr = n! / r! (n - r)!

n = # Total de objetos
r = # de objetos que selecciono

Question 103

PERMUTATIONS

En las permutaciones…

Answer 103

El orden SÍ importa.

Por lo general los problemas incluyen el “wording”: “ranking”, “order”, “arrange”.

Question 104

PERMUTATION FORMULA

Answer 104

nPr = n! / (n - r)!

Question 105

CONJUNTOS Y DIAGRAMAS DE VENN

Formula para relacionar “Dos Grupos”

Answer 105

G1 + G2 - Ambos + Ninguno = Total

Question 106

0!

Answer 106

1

Question 107

How many different anagrams are possible for the word ATLANTA?

Answer 107

3! 2!

*Tenemos múltiples repeticiones: tres A’s y dos T’s

Question 108

STATISTICS

Lo primero que hay que hacer cuando me piden “Median”

Answer 108

Ordenar los números en orden ascendente o descendente.

Median: es el número medio de un conjunto ordenado.

Question 109

STATISTICS

Mode

Answer 109

El número que aparece con más frecuencia en el conjunto de números.
Puede haber más de una Moda, o no puede haber Moda.

Question 110

STATISTICS

What is the sum of all even integers from 650 to 750, inclusive?

Answer 110

Sum of terms: (Mean) (Number of terms)

Mean (or Average) = Sum of the Terms / Number of Terms
Mean = Median -> el número de enmedio es 700.
50 + 1 = 51 (700) = 35,700

Question 111

FUNCTIONS
Qué tengo que contestar cuando me preguntan: “For which of the following values of x is f(x) defined? Indicate all such values”.

Answer 111

Debo analizar los términos que me den, cada uno. De tal forma que a partir de la naturaleza y características de cada uno de ellos, pueda empezar a eliminar opciones de respuesta hasta quedarme solo con las correctas.
A partir del término 5 / x+2, puedo saber que “x” no puede ser -2, porque las fracciones con denominador “0” son indeterminadas.

Question 112

Set A is the Set of all integers “x” satisfying the inequality 4 < |x| < 9
What are those?
What is the absolute value of the smallest integer in Set A?

Answer 112

Positive: 5,6,7,8. Four positive integers satisfy the inequality.
Negative: -5, -6, -7, -8. Four negative integers satisfy the inequality.

8 integers in Set A.
The smallest integer is -8. Its absolute value is 8.

Question 113

If the information in the answer choices supports the argument above, the the answer choices…

Answer 113

Must be PREMISES, and the Conclusion is found in the Argument.

Question 114

If the information in the body of the question supports the answer choices below, the Argument’s Conclusion…

Answer 114

The Argument’s Conclusion must be found in the answer choices (Inference question).

Question 115

If we are looking at an Inference Question, what is our first line of defense to get the correct answer?

Answer 115

The “NO new information” filter. The answer choices must be potential conclusions.
And Conclusions must be based entirely on the information based in the Premises. They basically restate information already given.

Question 116

(s^7) (t^7) =

Answer 116

(st)^7

Question 117

(w^5)^-3

Answer 117

w^15

Question 118

(x^-5) (y^5)

Answer 118

= (x^15)(y^-6)

x^15
= ————
y^6

Question 119

When solving a System of Equations for “x” and “y”, like this one:
15x - 18 - 2y = -3x + y
10x + 7y + 20 = 4x + 2
Remember:

Answer 119

18x - 3y = 18 (This one can make it smaller by factoring by 3).
6x + 7y = -18 (I multiply it by -1, so I can get rid of the new -6x)
That the first step is arrange the variables in one side, and the numbers alone on the other side.
And to align them up so I can get rid of one variable to solve for the other.

Question 120

Another way to write and see this fraction:
3x
—-
5

Answer 120

3
—- (x)
5

Question 121

If the Ratio of “2x” to “5y” is 3 to 4, what is the Ratio of “x” to “y”

Answer 121

15/8
Procedimiento = Cross Multiplication
8x = 15y
x/y = 15/8

Question 122

DISTANCE - RATE - TIME
“Two cars started from the same point and traveled on a straight course in opposite directions for exactly 2 hrs., at which time they were 208 miles apart. If one car traveled, on average, 8 m/h faster than the other car, what was the average speed for each car for the 2-hr trip?

Answer 122

Separate and organize the information given for each car:
1rst Car Data:
Rate = x m/h ; Time = 2 hrs ; Distance = 2x miles
2nd Car Data:
Rate = x + 8 m/h ; Time = 2 hrs ; Distance = 2(x + 8) miles
Equation:
Distance + Distance = 208 miles
2x + 2(x+8) = 208 —> And I’m ready to solve for “x”

Question 123

COORDINATE GEOMETRY

If we are asked to solve the equation of a line for “y”, then we automatically put the equation into:

Answer 123

Slope-Intercept form.

y = mx + b

Question 124

COORDINATE GEOMETRY
What is the Slope of the line with the equation
3x + 5y = 8?

Answer 124

We have to solve for "y", to put this into Slope-Intercept form: 
y = mx + b
3x + 5y = 8 ---> 5y = -3x + 8
"y" = 3/5x + 8/5
The Slope is "m" = - 3/5

Question 125

COORDINATE GEOMETRY
Horizontal lines have a Slope of zero, because they are all “run” with no “rise”.
So, if a horizontal line has a y-intercept of 4, then “m” and “b” =

Answer 125

“m” = 0
“b” = 4
They belong to the Slope Intercept form: y = mx + b

Question 126

COORDINATE GEOMETRY

What is the Slope of a Vertical Line?

Answer 126

Undefined, because the slope fraction is always:
(Something)/Zero
We cannot divide by zero.

Question 127

COORDINATE GEOMETRY
When trying to know the quadrants that contain a point of certain line represented by an equation, such as: x-y = 18, remember:

Answer 127

Work it out by rewriting the line in the Slop-Intercept form:
y = x-18
Then, set “x” and “y” to be “zero” and solve accordingly.
I must end with two points (2 numbers for each point).
When solving for “x”, “y” is zero.
When solving for “y”, “x” is zero.

Question 128

COORDINATE GEOMETRY

In order to find “the equation” of a line I have to consider:

Answer 128

y2 - y1
——— The result goes into the formula: y = mx + b
x2 - x1 where “+ b” is the point in which the line crosses the
y-axis.

Question 129

COORDINATE GEOMETRY

To find the coordinates of the point of intersection of two lines defined by some equation, I have to consider:

Answer 129

To work with the two equations given as a system of equations (by adding them up). The goal is to get both variables (x,y).
There is no need to graph the two lines to find the point of intersection.

Question 130

COORDINATE GEOMETRY
When trying to know which “Slope of the Line” is greater, I will be given Equation A, and Equation B.
What is the best approach?

Answer 130

To put each equation into Slope-Intercept Form (y = mx + b), and see which has the greater value for “m”.

Question 131

FRACTIONS

What is greater 2/-5 or 5/-2

Answer 131

2/-5
If I want to know which fraction is bigger, I have to let the negative sign to the number it originally belongs (not to the whole fraction as usual).
Then cross multiplication can work correctly.

Question 132

COORDINATE GEOMETRY

The distance between points, can be measured by:

Answer 132

I will be given two points for answer “A” and answer “B”.
Each two will construct a Right Triangle, then I can plug the proper values into the Pythagorean Theorem and solve for the Hypotenuse.

Question 133

GEOMETRY

What can I know if I’m told that “a” and “b” are complementary angles?

Answer 133

They sum to 90 degrees.

Question 134

GEOMETRY
When solving a Right Triangle problem, and if I’ve been given the Hypotenuse (c^2) and just one Leg (a^2), so I can solve for the second missing Leg, how do I work with it?
Example: 10, ?, 26

Answer 134

I have to work with the Pythagorean Theorem.
a^2 + b^2 = c^2
10   +   ?   = 26^2
100 + ?^2 = 676
?^2 = 576
?= 24     <- Correct Answer

Question 135

GEOMETRY

There is a cube with inside edges of 4, what is the diagonal of the cube?

Answer 135

4 Times Square Root of 3
1. Think about two Right Triangles: one located at the base of the cube, and the second one that has the actual “diagonal” required by the problem (its Hypotenuse).
2. Get the first Hypotenuse of the base Right Triangle:
4^2 + 4^2 = c^2
16 + 16 = Square root of 32
3. Get the second Hypotenuse of the second Right Triangle (which is the actual diagonal required):
4^2 + Square Root of 32, squared = Square Root of 48
Simplification: 4 Times Square Root of 3

Question 136

GEOMETRY

When working with Equilateral Triangles (3 equal sides, 3 equal angles), remember:

Answer 136

1. Two 30 - 60 - 90 “Special Right Triangles” are hidden. Those help me to get the area of the original Equilateral Triangle.
2. The Ratio of the “Special Right Triangle” is:
   Leg (1) Leg (2) Hypotenuse
   x - Square Root of 3 - 2x

Question 137

GEOMETRY

Any time you see a Right Triangle and one of the sides has a length of Square Root of 3, or a multiple of it…

Answer 137

I should check to see if it is a 30 - 60 - 90 degrees Triangle.

Question 138

GEOMETRY

When working with a Special Right Triangle: 30 - 60 - 90, how can I know which Vertex belong to 30 and 60 degrees?

Answer 138

30 degrees is opposite the short Leg.

60 degrees is opposite the long Leg.

Question 139

GEOMETRY
Usually, there are problems with a “fence” (valla), and “yard”story.
What they usually ask is:

Answer 139

To focus in the perimeter and the area.
Usually I have to work with the sides of a figure, such as: rectangle, or a square. The sides.
If I read: “one 40-foot side of the yard”, they are giving me one side of the figure (40).

Question 140

GEOMETRY
To find the Surface Area of a Rectangular Solid, (“… how much will it cost to cover the surface of the tank?”), I have to:

Answer 140

Sum the individual areas of all six faces. Top and Bottom, Side 1, and Side 2.
Usually, the problem will give three quantities to work with.

Question 141

GEOMETRY

The volume of a rectangular solid equals =

Answer 141

(Length) * (Width) * (Height)

Question 142

GEOMETRY

To find the surface area of a Rectangular Solid =

Answer 142

Sum the individual areas of all six faces.

Surface Area: 2(lw + lh + w*h)

Question 143

GEOMETRY

What is the volume of a Cube?

Answer 143

S^3

Question 144

GEOMETRY

What is the surface area of a Cube?

Answer 144

6s^2

Question 145

RATIO AND PROPORTIONS

When solving a “What is the Ratio” problem, remember:

Answer 145

I must respect the order in which the problem requires the ratio. For example: “What is the ratio of the cube’s surface area to its volume?”.
Answer: C’SA
——–
VOL

Question 146

GEOMETRY

What does it mean that: Square ‘efgh’, is INSCRIBED within square ‘ABCD’?

Answer 146

That square ‘efgh’ is perfectly inside a bigger square: ‘ABCD’.

Question 147

GEOMETRY

What is a Parallelogram?

Answer 147

It is a flat shape with opposite sides parallel and equal in length.

Question 148

GEOMETRY

Formula to get the Circumference of a Circle?

Answer 148

The Circumference of the Circle is “PI”d.
d = Diameter

Alternatively:

2’PI’r

Question 149

GEOMETRY
When solving a problem where the Surface Area of a Cylinder is involved, and I have to find the Diameter or the Radius of the Cylinder, remember:

Answer 149

1. Cylinder Surface Area formula: 2(‘PI’r^2) + 2’PI’rh

2. Very likely to get two results for r = (r+#) (r-#) I have to use the positive number.

Question 150

GEOMETRY

Formula to get the Volume of a Cylinder:

Answer 150

‘PI’r^2h

Question 151

GEOMETRY

How to get the Area of a Sector =

Answer 151

Angle of a Sector/380 times () the Area of the Circle -PIr^2-

Question 152

GEOMETRY

When working with solid shapes in which story they must be painted or covered for some substance, remember:

Answer 152

You are working with Surface Area.
If the story asks you to find the number of “paint buckets”, and by math you get a decimal as the answer, such as 10.2, remember stores do not sell fractional buckets, so you will need to purchase 11 buckets.

Question 153

GEOMETRY

When working with Circles, and you are asked to find the length of an Arc, remember:

Answer 153

1. You will be given an Angle, either Central (bigger number) or Inscribed (Smaller number). One is half the other, so with one of them you can get the other.
2. The Central Angle must be divided by 360, of the…
3. The Circumference of the Circle = PI*d

Question 154

GEOMETRY

Square Root of 1?

Answer 154

1

Question 155

GEOMETRY

The Sector of a Circle is:

Answer 155

The pizza slice.

Question 156

GEOMETRY

When finding a Circle Arc Length, remember:

Answer 156

Knowing the Center Angle and the Radius, I set up a proportion, cross multiply and solve the Arc Length:
Central Angle Arc Length
—————- = ——————
360 2’PI’ r

Question 157

NUMBER PROPERTIES
Seven people enter a race. There are 4 types of medals given as prizes for completing the race. The winner gets a platinum medal, the runner- up gets a gold medal, the next two racers each get a silver medal, and the last 3 racers all get bronze medals. What is the number of different ways the medals can be awarded?

Answer 157

Anagram Grid:
1  2   3  4  5  6  7
P  G  S  S B B  B
Translate into Factorials:
7!
-----
1! 1! 2! 3!
The numerator of the fraction is the factorial of the largest number in the top row, in this case 7!.

Question 158

COMBINATORICS
“Or”, means:

“And”, means:

Answer 158

1. OR means add.

2. AND means multiply.

Question 159

COMBINATORICS
A local card club will send 3 representatives to the national conference. If the local club has 8 members, how many different groups of representatives could the club send?

Answer 159

Anagram Grid
1   2   3   4   5   6   7   8 
Y  Y   Y   N  N   N  N  N
Then, set a Factorial Fraction
8!
-----
3! 5!
There are 3 representatives chosen; represent them with Y. Use N to represent the 5 members of the group who are not chosen.

Question 160

GEOMETRY

When working with Square Roots, remember:

Answer 160

To check if the number inside the root can be simplified.
For example: Square Root of 98.
It can be simplified to 7 times Square Root of 2.
Use Prime Factorization to determine it:
98 = 2x7x7

Question 161

GEOMETRY

The sum of the measures of the interior angles of a polygon with “n” sides is:

Answer 161

(n-2) * 180
For example: a Hexagon has 6 sides. Therefore, substitute 6 for “n” into the formula an calculate.
(6-2) * 180 = 720
Therefore, the sum of the measures is 720.

Question 162

GEOMETRY

Equilateral Triangles have three interior angles of:

Answer 162

60 degrees.

Question 163

VARIABLES AND NUMERICAL PROVE

Which are good numbers to try in a problem?

Answer 163

1, 2, 0, -1, -2, 1/2

Question 164

WORD PROBLEMS

Velocidad es:

Answer 164

La Distancia dividida entre el Tiempo.

Question 165

WORD PROBLEMS

Speed Formula

Answer 165

Time

S = D/T

Question 166

WORD PROBLEMS

Distance =

Answer 166

(Speed) (Time)

Question 167

WORD PROBLEMS

Time =

Answer 167

Speed

Question 168

WORD PROBLEMS
When to objects approach or leave to each other from different directions, along the same route, the speed they are approaching is:

Answer 168

The sum of their individual speeds.
Car 1 travels at 40 mph; Car 2 travels at 50 mph, the distance between the Cars is reduced at a rate Speed of 40 + 50 = 90 mph

Question 169

WORD PROBLEMS
Cuando un objeto que se mueve a una velocidad más rápida se acerca por detrás a uno que se mueve (por la misma ruta), más lentamente, la velocidad a la que el rápido se acerca al lento es:

Answer 169

La Diferencia entre sus velocidades individuales.
Si un camión viaja a 25 mph y el otro a 35 mph, la Distancia entre ellos se reduce a una tasa de 35 - 25 = 10 mph.
Una vez que el rápido rebasa al lento, la Distancia entre ellos crece a una tasa de 10 mph.

Question 170

WORD PROBLEMS

Paso 1 para resolver un problema de Distance, Speed, Time:

Answer 170

Asigna Variables.

Question 171

WORD PROBLEMS

How many minutes is 1/4 of an Hour?

Answer 171

15 minutes

1/4 * 60 (minutes) = 15 minutes

Question 172

WORD PROBLEMS

Si una Década se expresa matemáticamente como 10/10, ¿cómo se expresarían dos Décadas?

Answer 172

20/10

Question 173

WORD PROBLEMS

How many minutes is 1/4 of an Hour?

Answer 173

15 minutes

1/4 * 60 (minutes) = 15 minutes

Question 174

WORD PROBLEMS

Cuál es la fórmula de crecimiento exponencial?

Answer 174

A, “dos” = A, “uno” x f^t/T
t = Punto en el tiempo que busco.
T= El tiempo que le toma a A, “uno” crecer (o decrecer) f veces sí misma.
Ex. A certain bacteria triple in number every 20 min. How long will it take a million such bacteria to reach 27 million in number?
27 = 1 x 3^t/20
3^3 = 3^t/20 —–> 3 = t/20
t = 60 minutes

Question 175

WORD PROBLEMS

El primer paso para resolver un problema:

Answer 175

Estandarizar las unidades.
1 km = 1000 mts
2 km = 2(1000) mts
1 hr = 60 min

Question 176

WORD PROBLEMS

El primer paso para resolver un problema:

Answer 176

Estandarizar las unidades.
1 km = 1000 mts
2 km = 2(1000) mts
1 hr = 60 min

Question 177

GEOMETRY

To find the length of an Arc of a Circle…

Answer 177

First, I need to calculate the Circumference of the Circle: 2’PI’* radio.
Divido los grados del Arco “entre” 360 grados. Si el resultado es fracción, por ejemplo 1/6, entonces multiplico el resto contrario de 5/6 “por” la Circunferencia.

Question 178

GEOMETRY

When asked to get the Area of a Parallelogram, remember:

Answer 178

Inside, it might has two congruent (identical) Right Triangles.
So you can get the Parallelogram’s Area by getting one Right Triangle’s Area, and multiply it by 2 (because there are two equal Right Triangles in total).

Question 179

GEOMETRY

When asked to solve a problem between two Rectangular figures, remember:

Answer 179

One of them might be a Square.

It is not necessary to work with to Rectangles.

Question 180

GEOMETRY

¿Diferencia entre el Diámetro de un Círculo y la Cuerda (Chord) de un Círculo?

Answer 180

El Diámetro es la Cuerda (Chord) más larga que se puede dibujar en un Círculo. Va de lado a lado.
Por su parte, la Cuerda (Chord) puede ser más pequeña que el Diámetro.

Question 181

GEOMETRY

The Slope is defined as…

Answer 181

Change in “Y” / Change in “X”

Question 182

GEOMETRY
En el ‘Coordinate Plane’ me pueden preguntar por los posibles valores de ‘X’, con los que una ecuación como: y=x^3-x^2-6x, toca el x-axis?

Answer 182

Para resolver estas preguntas es nevesario establecer a “y” como cero.
Posteriormente factorizar una ‘x’ y trabajar por las dos raíces.
0 = x (x+2) (x-3)
Hence, y = 0 when x = 0, -2, or 3.
Uno o varios de estos números estarán en las respuesta correcta.

Question 183

GEOMETRY

¿Qué es un Obtuse Angle?

Answer 183

Un ángulo con una medida mayor a los 90 grados.
Forma parte de un Triángulo, que vive en el Plano.
Para reconocer un ángulo obtuso en el ‘Coordinate Plane’, es necesario primero tener dos puntos. El tercer punto forma el Triángulo. Si éste esta más arriba o más abajo de los dos puntos, entonces el Triángulo tendrá un ángulo obtuso.

Question 184

GEOMETRY

Cuando de un Cuadrado sólo sé que su diagonal es ‘x’, debo recordar que:

Answer 184

1. La diagonal divide al Cuadrado en dos Triángulos Isóceles (45-45-90).
2. El ratio de un lado del cuadrado y la diagonal es: 1 : Raíz Cuadrada de 2.
3. Puedo encontrar la medida de un lado del Cuadrado, dividiendo
   x / Raíz Cuadrada de 2
4. Raíz Cuadrada de 2 es aproximadamente 1.4, o bien, 7/5
5. x / 7/5 ———> 5x / 7

Question 185

GEOMETRY

¿Cuál es la suma de los ángulos de un Cuadrilátero?

Answer 185

360 grados.

Question 186

GEOMETRY

¿Cómo calcular dos ángulos restantes en un Cuadrilátero inscrito en un Círculo?

Answer 186

El problema me ha dado ya dos ángulos. Por ejemplo uno de 60 grados y el segundo de 110. Si les sumamos el ángulo opuesto de cada uno de ellos el resultado es 180 grados.
Así, el ángulo opuesto al ángulo de 60 grados, es 120, porque
120 + 60 = 180
El ángulo opuesto a 110 es 70 porque 110 + 70 = 180

Question 187

GEOMETRY
Cuanto me enfrente a Círculo A y Círculo B, ambos inscritos en
Círculo C, recuerda:

Answer 187

Si todos comparten la misma línea de Diaámetro, no sumo los “PI” de cada uno de ellos. El “PI” se factoriza, de tal dorma que
Diámetro Uno + Diámetro Dos = Diámetro Tres

Question 188

GEOMETRY

What is the conversion relation from Feet to Inches?

Answer 188

1 Feet = 12 Inches

Question 189

SQUARE ROOT OF 3?

Answer 189

1.7

Question 190

WORD PROBLEMS

The words ‘is’, or ‘are’ in the text correspond to:

Answer 190

The Equal sign: =

Question 191

WORD PROBLEMS

Translate mathematically, “A is 50 more than B”

Answer 191

A = B + 50

Question 192

WORD PROBLEMS

Translate: “A is 50% of B”

Answer 192

A = 0.5B
Or —> This is a good opportunity to multiply both sides by 2:
2A = B

Question 193

WORD PROBLEMS

Translate: “A is 50% greater than B”:

Answer 193

A = 1.5B

Question 194

WORD PROBLEMS

Translate: Right now, Steve’s age is half of Tom’s age.

Answer 194

S = T / 2
But more conveniently, we avoid fractions:

T = 2S <—– This is way more convenient to work with.

Question 195

WORD PROBLEMS

Set the equation: “In eight years, twice Tom’s age will be five more than three times Steve’s age”.

Answer 195

2 (T + 8) = 3 (S + 8) + 5
Important: I have to choose variables to represent the ages NOW, and use ADDITION and SUBTRACTION to create expressions for ages at other times.
In this case, “+ 8”.

Question 196

WORD PROBLEMS
What does this variables stand for?
D = RT

Answer 196

D = RT, is the formula for solving Motion Questions.
D = Distance
R = Rate or Speed
T = Time
*I can easily solve for R or T.

Question 197

WORD PROBLEMS
Meters to Centimeters equivalence:
1 m =

Answer 197

100 cm

Question 198

WORD PROBLEMS
Hour to Seconds, equivalence.
1 HR =

Answer 198

3600 Sec

Question 199

WORD PROBLEMS
“A car moving at 72 km/hr moves how many meters in one second?”.
(1km = 1000 m)

Answer 199

1. 1 hr = 3600 s
2. Rewrite the proportion with the problem units:
   72 km/hr = 72,000 m / 3600 s
   *To change 72 km to m, I just multiply 72 km * 1000 m = 72,000 m
   Correct Answer: 20 m/s

Question 200

WORD PROBLEMS

Average Velocity / Speed Formula =

Answer 200

Total Distance / Total Time

Question 201

WORD PROBLEMS

“Bob drove 120 miles at 60 mph, then another 120 at 40 mph. What was his AVERAGE SPEED for the TOTAL trip?”

Answer 201

48 mph —> The formula: Total Distance / Total Time

1. First Leg, D =120 miles.
2. Get the Time of First Leg, D. T = D/R —> T = 120 m / 60 mph = 2hr
3. Second Leg, D = 120 miles.
4. Get the Time of Second Leg, D. T = D/R —> 120 m / 40 mph = 3 hr
5. Total Distance / Total Time = 120 m + 120 m / 2 hr + 3 hr = 48 mph

Question 202

WORD PROBLEMS
In Average Speed problems, sometimes I don’t get to know the Distance or Speed values, so I can add them up into the Average Speed formula: Total Distance / Total Time.
What do I do?

Answer 202

Still, work with the variable you don’t have.
If “Emma drove from A to B at a constant 60 mph speed. Then returned on the same route at a constant speed of 20 mph”.
T-One = D / R = D / 60
T-Two = D / R = D / 20
Total Time = T-One + T-Two = D/15
Average Speed = 2D / [D/15] = 30 mph

Question 203

GEOMETRY
Set the equation of “Martha and Paul started traveling from A to B at the same time. Martha traveled at a constant speed of 60 mph, and Paul at a constant speed of 40 mph. When Martha arrived at B, Paul was still 50 miles away. What is the distance between A and B?”.

Answer 203

D = RT —> D = 60T D - 50 = 40T
60T - 50 = 40T
20T = 50
T = 2.5 hr
D = 60*(2.5) = 150 miles

Question 204

WORD PROBLEMS

When a Word Problem involves multiple travelers, multiple trips, or a trip with multiple legs, remember:

Answer 204

That each traveler, each trip, and Leg, deserves its own D = RT equation.

Question 205

WORD PROBLEMS

What is the Work Equation?

Answer 205

A = RT
A = Amount of work done. (Products manufactured, houses painted, pizzas made, etc.)
R = The work rate. (Number of products per minute, houses per day, pizzas per hour, etc).
T = Time

Question 206

WORD PROBLEMS
“When Amelia and Brad detail a car together, 1 car takes 3 hrs. When Amelia details a car alone, 1 car takes 4 hrs. How long does it take Brad, working alone, to detail one car?”.

Answer 206

Rates = Cars / Hours
1/4 + 1/x = 1/3 —> 1/x = 1/3 - 1/4 —> 1/12
Brad = 1/12

Question 207

WORD PROBLEMS

“How much HCL and how much water must we use to create 5 Liters of a 30% HCL solution?”.

Answer 207

The amount of HCL would be 30% as a decimal times the Whole:
0.30*5 = 1.5 Liters of pure HCL.
This means that the rest of the solution would require the following amount of water: 5 Liters - 1.5 Liters of pure HCL = 3.5 Liters of water.

Question 208

WORD PROBLEMS

“Suppose we start with 5 liters of a 30% HCI solution. How much water must we add to create a 20% solution?”.

Answer 208

Amount of HCL = 0.30 * 5 = 1.5 liters
In the new solution:
Amount of HCI = 0.20 * x = 1.5 liters (1.5 liters of HCL. It does not change because all we are adding is water).
x = 7.5 liters total, which is the amount of the new solution.
Added water = 7.5 - 5 = 2.5 liters of extra water required to bring from 30% to a 20% solution.

Question 209

WORD PROBLEM
“Suppose we start with 8 liters of a 60% HPO solution. We add 4 liters of x% HPO solution, and the result is 12 liters of a 50% HPO solution. What is x?”.

Answer 209

1. Get how much HPO I begin with, and how much I end with.
   Begin: 0.60 * 8 = 4.8 liters
   End: 0.50 * 12 = 6 liters
   Therefore, HPO (also called “solute”: sustancia disoluta), added: 6 - 4.8 = 1.2 L
   Finally, I have to figure out 1.2 is what per cent of 4 = 30%
   x = 30%

Question 210

SKILL:

-3x = -7, what is “x”?

Answer 210

x = 7/3, the negative signs cancel out.

Question 211

WORD PROBLEMS
“We start with unlimited supplies of a 20% HSO solution, and of a 50% HSO solution. We combine “x” liters of the first with “y” liters of the second to produce 7 liters of a 40% HSO solution. What does “x” equal?”.

Answer 211

Because there are two different solutions, I have to set up simultaneous equations. One will always be the “total” equation.
x + y = 7 liters.
The other equation will always be about the amount of solute:
.20x + .50y = 2.8

Question 212

SKILL:
How can I make this equation easier to solve?
0.2x + 0.5x = 2.8

Answer 212

By getting rid of the decimals by multiplying everything by 10:
2x + 5x = 28

Question 213

GEOMETRY

How to calculate any Arc Length?

Answer 213

x/360 * 2 ‘PI’ r

Question 214

GEOMETRY

How to calculate any Sector?

Answer 214

X/360 * ‘PI’ r^2

Question 215

PRIME NUMBERS BETWEEN 2 AND 7, INCLUSIVE?

Answer 215

2,3,5,7

Question 216

PRIME NUMBERS BETWEEN 11 AND 19, INCLUSIVE?

Answer 216

11,13,17,19

Question 217

PRIME NUMBERS BETWEEN 23 AND 29, INCLUSIVE?

Answer 217

23, 29

Question 218

PRIME NUMBERS BETWEEN 31 AND 37, INCLUSIVE?

Answer 218

31, 37

Question 219

PRIME NUMBERS BETWEEN 41 AND 47, INCLUSIVE?

Answer 219

41, 43, 47

Question 220

PRIME NUMBERS BETWEEN 53 AND 59, INCLUSIVE?

Answer 220

53, 59

Question 221

PRIME NUMBERS BETWEEN 61 AND 67, INCLUSIVE?

Answer 221

61, 67

Question 222

PRIME NUMBERS BETWEEN 71 AND 79, INCLUSIVE?

Answer 222

71, 73, 79

Question 223

PRIME NUMBERS BETWEEN 83 AND 89, INCLUSIVE?

Answer 223

83, 89

Question 224

PRIME NUMBER BEFORE 100 AND IN THE 90’S TEN?

Answer 224

97

Question 225

FIRST PRIME NUMBER AFTER 100?

Answer 225

101

Question 226

WORD PROBLEMS: MATRIX METHOD FOR GROUPING AND SET
“In a company of 300 employees, 120 are females. A total 200 employees have advanced degrees, and the rest have college degree only. If 80 employees are males with college degree only, how many are females with advanced degrees?”.

Answer 226

Females Males Total
College Only 20 80 100

Advanced Degree 100 100 200

Total 120 180 300
* This method simplify problems in which each member is placed into two different kinds of categories.

Question 227

WORD PROBLEMS
Sometimes in 3 circled Venn Diagram problems, I might find as on portion of the problem something like this: "... If 220 students are in either Italian class or Baseball...". 
What does this mean?

Answer 227

“Italian class or Baseball”, means that all the regions in the circle “Italian Class”, and all the regions in the circle “Baseball” add up to equal 220.

Question 228

WORD PROBLEMS

“Find the 41st term of the sequence: 14, 23, 32, 41, 50, 59…”

Answer 228

1. a-One = 14
2. Difference between terms: 9
3. Formula: a-“n” = a-One + d*(n-1)
4. Apply the Formula: a-Forty First = 14 + 9(n-1) = 14 + 9(40)
5. 41st term is 374

Question 229

WORD PROBLEMS

Skill: when working with RECURSIVE SEQUENCES (for example Each term ‘sub’ n-1), remember:

Answer 229

Each term is defined in terms of one or two previous terms.
There is no way to jump immediately to the value of term. Instead, I have to find each and every term from the start up to the desired term.

Question 230

WORD PROBLEM

“How many multiples of 8 are there from 200 to 640, inclusive?”

Answer 230

1. Divide 200 / 8 = 25
2. Divide 640 / 8 = 80
3. 80 - 25 + 1 (I add 1) = 56
4. 56 multiples of 8 starting at 200 and going up all the way to 640.

Question 231

WORD PROBLEMS

“What is the sum of all the multiples of 20 from 160 to 840, inclusive?”

Answer 231

1. 160 / 20 = 8 (the eight multiple of 20)
2. 840 / 20 = 42 (the 42nd multiple of 20)
3. Inclusive Counting step: 42 - 8 + 1 = 35
4. 35 / 2 = 17.5
5. Answer the question: 17.5 * (160 + 840) = 17,500

Question 232

COMMON WORD PROBLEM PHRASES

“The Profit is the Revenue minus the Cost”

Answer 232

P = R - C

Question 233

COMMON WORD PROBLEM PHRASES

“n persons have x beads (perlas) each. “The total number of beads is”

Answer 233

nx

Question 234

COMMON WORD PROBLEM PHRASES

“Five dollars every two weeks”

Answer 234

5 dollars / 2 weeks

—> 2.5 dollars a week

Question 235

COMMON WORD PROBLEM PHRASES

“There are twice as many computers as there are printers”

Answer 235

C = 2P

Question 236

COMMON WORD PROBLEM PHRASES

“Container A is three times as big as Container B”

Answer 236

A = 3B

Question 237

COMMON WORD PROBLEM PHRASES

“One half of the students are learning French”

Answer 237

F = 1/2S

Question 238

COMMON WORD PROBLEM PHRASES

“The are 10 more Grapes than Apples, and 1/4 as many Apples as Pears”

Answer 238

G = A + 10, and A = 1/4 P

Question 239

COMMON WORD PROBLEM PHRASES
“Three friends sit down to eat 14 slices of pizza. If two of the friends eat the same number of slices, and the Third eats two more slices than each of the other two, how many slices are eaten by the Third friend?”.

Answer 239

F + F + T = 14 slices of pizza.
T = F + 2
F + F + F + 2 = 14
F = 4
Therefore, T = 6
                  *Sustituir T por un amigo individual.

Question 240

WORD PROBLEMS

PROFIT =

Answer 240

Revenue - Cost

Question 241

WORD PROBLEMS
“Arnaldo earns $11 for each ticket that he sells, and a bonus of $2 per ticket for each ticket he sells over 100. If Arnaldo was paid $2,400, how many tickets did he sell?”.

Answer 241

Let x = the total number of tickets sold.
Therefore, (x - 100) = the number of tickets sold over 100.
11x + 2 (x - 100) = 2,400
x = 200

Question 242

SKILL:

TOTAL REVENUE

Answer 242

Ingresos Totales

Question 243

WORD PROBLEMS

Breaking even occurs when…

Answer 243

When total revenue equals total cost.

Question 244

WORD PROBLEMS
“Every week, Renee is paid $40 per hour for the first 40 hours she works, and 80 dollars per hour for each hour she works after the first 40 hours. If she earned $2000 last week, how many hours did she work?”.

Answer 244

Let h = number of hours Renee worked.
40(40) + (h-40) (80) = 2000 -assuming h = 40.
1,600 + 80h - 3,200 = 2000
80h - 1,600 = 2000
80h = 3,600
h = 45

Question 245

WORD PROBLEMS
En Problemas de Edad recuerda que ocasionalmente tienes que pensar en “escenarios extrmos”.
Jane started baby-sitting when she was 18. Whenever she baby-sat for a child, that child was no more than half her age at the time. Jane is currently 32, and she stopped baby-sitting 10 years ago. What is the current age of the oldest person for whom Jane could have baby-sat?”.

Answer 245

23
Tengo la edad actual de Jane: 32. Debo pensar en escenarios extremos.
A los 18 pudo cuidad a un niño de máximo 9. Hoy este niño tendría 23 años.
El otro extremos es que a los 22 ella pudo cuidar a un niño de máximo 11 años, por lo que 10 años después éste tiene 21 años.
23 > 21

Question 246

WORD PROBLEMS
Cuando el problema hable sobre un “tank” al que se pretende llenar con agua, y cuyas medidas me son proporcionadas: “If the tank is 6 ft. long, 4 ft. wide, and 8 ft. deep, how many hours will it take to fill up the tank?”.

Answer 246

La capacidad del tanque se obtiene multiplicando:
6 ft. long x 4 ft. wide x 8 ft. deep = 192
After this step, to solve the problem I could use the formula RT = W
In this case W would be substituted for 192 cubic feet.

Question 247

WORD PROBLEMS
SKILL: En problemas de “crecimiento exponencial” recuerda que un método que funciona para llegar a la respuesta correcta es:

Answer 247

Enlistar los valores correspondientes a cada crecimiento.

Hacer listas ayuda a encontrar la respuesta “aproximada” correcta.

Question 248

SKILL: Recuerda que si divido 18/7, en ocasiones no hay porqué llegar a los decimales.

Answer 248

Se puede quedar en una “mixed fraction” :

2 4/7

Question 249

WORD PROBLEMS

In “working together” problems recuerda:

Answer 249

Add the individual Rates.

Then, use the RT = W equation to find the total work done.

Question 250

WORD PROBLEMS

Remember: The Average Rate is equal to…

Answer 250

The total work done divided by the time in which the work was done.

Question 251

WORD PROBLEMS
When facing a “kiss” problem: when to objects are approaching to each other I work with a RTD Chart.
“A train leaves Kyoto for Tokyo traveling 240 m/h at 12 noon. Ten minutes later, a second train leaves Tokyo for Kyoto traveling 160 m/h. If Tokyo and Kyoto are 300 miles apart, at what time will the trains pass each other”.

Answer 251

R x T = D
Train: K to T 240 m/h t + 1/6 = 240t + 40
Train: T to K 160 m/h t = 160t
Total: = 300
Now, sum the Distances:
400t = 260 —> t = 13/20 —>
multiply everything by 3 = 39/60
Answer: 39 minutes

Question 252

WORD PROBLEMS

A way to solve an Average Speed problem.

Answer 252

By using a Multiple RTD chart.
R x T = D
A to B
B to A
A to B
I have to get all the Individual Times, and the Total Distance.
If necessary I can chose SMART numbers for the Distance (a common multiple for the Rates in the problem).

Question 253

WORD PROBLEMS

SKILL: Para responder problemas de mangueras (hose) que llenan albercas con agua (y problemas de trabajo), recuerda:

Answer 253

Me puedo apoyar en un chart R x T = W
Abajo de “R” pongo la suma de los Rates de las mangueras.
Si una manguera llena una alberca en 6 horas, el Rate es 1/6 por hora.
En “W” podría ir, por ejemplo, el Work que el problema me pida hacer.

Question 254

STATISTICS

What is the Mean?

Answer 254

The sum of the numbers divided by the number of terms.

Question 255

STATISTICS

What is the Median?

Answer 255

It is the Middle number.

Question 256

STATISTICS
"The class Mean score on a test was 60, and the Standard Deviation was 15. If Elena's score was within 2 Standard Deviations of the Mean, what is the lowest score she could have received?".

Answer 256

30
Elena’s score was within 2 standard deviations of the mean. Since the standard deviation is 15, her score is no more than 30 points from the Mean. The lowest possible score she could have received, then, is 60-30 = 30

Question 257

STATISTICS

What is the set of the first five positive even integers?

Answer 257

2,4,6,8,10

No zero, because it is even but not positive nor negative.

Question 258

COMBINATORICS

In how many different ways can the letters in the word “LEVEL” be arranged?

Answer 258

30
There are two repeated "E" and two repeated "L" in the word "LEVEL". To find the anagrams for this word, set up a fraction in which the numerator is the factorial of the number of letters and the denominator is the factorial for the number of each repeated letter.
5!
----- = 30
2! 2!

Question 259

COMBINATORICS
“Amy and Adam are making boxes of truffles to give out. They have an unlimited supply of 5 different types of truffles. If each box holds 2 truffles of different types, how many different boxes can they make?”.

Answer 259

10
In every combination, two types of truffles will be in the box, and three type of truffles will not. Therefore, this problem is a question about the number of anagrams that can be made from the "word" YYNNN:
5!
------ = 10
2! 3!

Question 260

COMBINATORICS
“A men’s basketball league assigns every player a two-digit number for the back of his jersey. If the league uses only the digits 1-5, what is the maximum number of players that can join the league such that no player has a number with a repeated digit (e.g. 22), and no two players have the same number?”.

Answer 260

20
In this problem, the order of the numbers matters. Each number can be either the tens digit, the units digit, or not a digit in the number. Therefore, this problem is a question about the number of anagrams that can be made from the "word", TUNNN.
5!
-------- = 20
1! 1! 3!

Question 261

COMBINATORICS
“A pod of 6 dolphins always swims single file, with 3 females at the front and 3 males in the rear. In how many different arrangements can the dolphins swim?”.

Answer 261

36
There are 3! ways in which the 3 females can swim. There are 3! ways in which the 3 males can swim.
Therefore, there are 3! x 3! = 6 x 6 = 36

Question 262

COMBINATORICS
“Mario’s pizza has two choices of crust. The restaurant also has a choice of 5 toppings. Finally, Mario’s offers every pizza in extra-cheese as well as regular. If Linda’s team decides to order a pizza with four toppings, how many different choices do the teammates have at Mario’s Pizza?”.

Answer 262

20
Consider the toppings first. Model the toppings with the “word” YYYYN, in which 4 of the toppings are on the pizza and one is not. The number of anagrams for this “word” is:
5!
—— = 5
1! 4!
If each of the pizzas can also be offered in 2 choices of crust, there are 5 x 2 = 10 pizzas. The same logic applies for extra-cheese and regular: 10 x 2 = 20

Question 263

COMBINATORICS
“Country X has 4-digit postal code assigned to each town, such that the first digit is non-zero, and none of the digits is repeated. What is rhe number of possible postal codes in Country X?”.

Answer 263

4,536
The first slot can be filled by any one of the digits from 1 to 9, since 0 is disallowed. The second digit has no restriction involving zero; however, the digit that was used in the first slot may not be used. Thus, the second slot also has nine possibilities. The third and fourth slots may not use previously used digits, so they may be filled with 8 and 7 different digits, respectively.
Total number of possible postal codes: 9 x 9 x 8 x 7 = 4,536

Question 264

COMBINATORICS
“8 athletes compete in a race in which a Gold, a Silver, and a Bronze medal will be awarded to the top three finishers, in that order. What is the number of ways in which the medals can be awarded?”.

Answer 264

336
Anagram Grid: in the first row we can use the numbers 1 to 8 to uniquely designate each athlete. In the second row, G, S, and B designate the three medals; while the athletes who get no medal can each be associated with an “N”.
Athlete: 1 2 3 4 5 6 7 8
Medal: G S B N N N N N
Because 5 of the letters are repeated, the answer is give by
8!/5! = 8 x 7 x 6 = 336

Question 265

COMBINATORICS
“Lothar has 6 stamps from Irapuato and 4 stamps of Cancún in his collection. He will give two stamps of each type to his friend Peggy. What is the number of ways Lothar can give four stamps (two of each type) to Peggy?”.

Answer 265

90
This is a successive "pick a group" problems. First, Lothar picks 2 out of 6 Irapuato stamps, and then 2 out of 4 Cancún stamps. Each selection may computed according to the general formula:
Pool!           Pool!
--------- * ----------- = 90
In! Out!       In! Out!

Question 266

COMBINATORICS
And =
Or =

Answer 266

And = Multiply
Or = Add

Question 267

PROBABILITY

How many ways there are in which 2 dice can be thrown?

Answer 267

(6 x 6) = 36

Question 268

COMBINATORICS

A small group drawn from a large group is a:

Answer 268

It is a Combination.

And in Combinations we don’t care about the order of selection. All we care is the final arrangement that we get.

Question 269

COMBINATORICS

What does the notation ‘nCr’, means?

Answer 269

This is often read as “n Choose r”.
If we have a group of n different individuals, and we randomly select r of these individuals, then the number of combination is denoted as:
nCr
For example: 8C3 would be the number of different 3-Person combinations we could select from a pool of eight.

Question 270

COMBINATORICS

nC1 =

Answer 270

n.

For example: 7C1 = 7 = The number of different ways I can choose one person from a pool of 7.

Question 271

COMBINATORICS

We have a pool of 10 different items, and we want to select a set of 4. How many different sets of four could we pick?

Answer 271

I have to think about ‘10C4’.
First, Fundamental Counting Principle (FCP): N = 10987, and because the order of the 4 selected doesn’t matter, I divide by 4!
10987
10C4 = ———— = 210
4321
Just compute1098*7 would be correct if order mattered.

Question 272

COMBINATORICS
“An amusement park has 12 different major rides. A coupon gives its holder access to any 3 of these rides for free. How many sets of three rides are possible?”.

Answer 272

220.
12C3 = 12 * 11 * 10
Then, divide by 3! = 6

Question 273

COMBINATORICS

Name a case in which order matters in a problem.

Answer 273

Different people in different roles, such in a leadership teams.
One guideline is to consider the resulting arrangement and whether switching items around in this result would matter.

Question 274

COMBINATORICS
“A librarian has a set of ten books, including four different books about Abraham Lincoln. The librarian wants to put the ten books on a shelf with the four Lincoln books next to each other, somewhere on the shelf. How many different arrangements of the ten books are possible?”.

Answer 274

(4!) (7!)
Since the four books must be together, think of them as one BIG book. There are six other books, and one BIG Lincoln book. In how many ways can we put these seven books in order on a shelf? Of course, 7!
After, we still can put the four Lincoln books in any order. There are 4! orders for the Lincoln books.
Total arrangements = N = (4!) (7!)

Question 275

COMBINATORICS
(Permutation problem example)
“From a group of 10 committee members, three will be randomly selected: one as chair, one as treasurer, and one as secretary. These three will form the “board” of the committee. How many different possible “boards” can be formed?”.

Answer 275

The Fundamental Counting Principle is a much more efficient way to solve the problem.
10 9 8
—– —– —– = 1098 = 720 possible boards.
C T S

Question 276

COMBINATORICS

Permutations VS. Combinations VS. FCP

Answer 276

1) The FCP is more basic, flexible, and more widely applicable than Permutations and Combinations.
2) If picking with no repeats, ORDER DOESN’T MATTER, then use Combinations.
3) If picking with no repeats, and different orders of the final selection are meaningfully different (i.e. ORDER MATTERS), then it’s a Permutation: use FCP.

Question 277

PROBABILITY

If two events, say A and B are “mutually exclusive” then the Probability of A or B -P (A or B)-, equals =

Answer 277

The Probability of A + The Probability of B

P (A) + P (B)

Question 278

PROBABILITY

What happens if events A and B are not mutually exclusive?

Answer 278

This means there is some “overlap” region counted twice; some occasions when both A and B can happen together.
Therefore, we need to subtract it once from the sum of the two regions.
Therefore, the Generalized OR Rule is:
P(A or B) = P(A) + P(B) - P(A and B)

Question 279

PROBABILITY

Which are the two “OR” rules?

Answer 279

1) The simple “OR” rule (for mutually exclusive events only).
P(A or B) = P(A) + P(B)
2) The Generalized “OR” rule (always works, for any events).
P(A or B) = P(A) + P(B) - P(A and B)

Question 280

PROBABILITY
“In Game M, the probability of outcome A is 0.6, the probability of outcome B is 0.7, and the probability of A or B is 0.9. What is the probability of A and B happening at the same time?”.

Answer 280

0.4
Generalized OR rule: 
P(A or B) = P(A) + P(B) - P(A and B)
         0.9 = 0.6 + 0.7 - P(A and B)
  P(A and B) = 0.6 + 0.7 - 0.9 = 0.4

Question 281

PROBABILITY

If events A and B are independent, then what rule can I use?

Answer 281

The simplified AND rule:

P(A and B) = P(A) * P(B)

Question 282

PROBABILITY

What is the notation for conditional probability?

Answer 282

P (A | B)
-For events NOT independent-
It means: “Assuming that, we know that event B is true, then given this condition, what is the probability that A happens?”
Or more briefly, “What is the probability of A, given B?”.

Question 283

PROBABILITY

What is the generalized AND rule:

Answer 283

P (A and B) = P(A) * P(B|A)
Or,
P(A and B) = P(B) * P(A|B)

*Used when A and B are NOT independent.

Question 284

SKILL: Antes de multiplicar una fracción:

Answer 284

Puedo simplificarla de forma “cruzada”.
5/12 * 4/11
= 5/3 * 1/11 = 5/33

Question 285

PROBABILITY

When I see the words “AT LEAST”, use the shortcut:

Answer 285

The Complement Rule: P(not A) = 1 - P(A)
The probability of not getting a six in one dice roll is (5/6).
The probability of not getting a single six in eight rolls is (5/6)^8.
Answer: P(at least one six) = 1-(5/6)^8

Question 286

SKILL

What are the answer options of the Quantitative Comparison Questions?

Answer 286

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Question 287

Simplify, 2^29 + 2^29 =

Answer 287

2 (2^29) = 2^30

*It works just with number 2

Question 288

PERMUTATION PROBLEM
“Five stand-by passengers are waiting for three open seats on an airplane flight. In how many different ways can three passengers be arranged in these seats?”.

Answer 288

60
I can just compute: 5x4x3= 60
Or, use the formula Pool! / Out!, where Out! Is the number of items NOT to be chosen: 5! / 2! = 60
*This is a problem in which order matters.

Question 289

PROBABILITY

When two fair dice are rolled, what is the probability that at least one of the numbers will be even?”.

Answer 289

Pay attention to “at least” problems. In such cases is easier to use the “1-x” shortcut (the probability of the event NOT happening).
The Probability of each number coming up odd is 3/6 = 1/2. Since the two dice are independent, the probability of both coming up is
1/2*1/2 = 1/4, so the probability of getting at least one even number is
1 - 1/4 = 3/4.

Question 290

In the proportion:
Vinegar Oil Water
14 21 15
At least what percent of the dressing will be vinegar?

Answer 290

28% of the mixture.
Vinegar Oil Water
14 21 15 = 50
Therefore, Vinegar makes up 14/50 = 7/25 = 0.28 * 100 = 28%

Question 291

“A child must choose from among 5 balloons, each of a different color. What is the number of combinations of three different balloons he can choose?”.

Answer 291

10
The number of ways that a child can choose a set of 3 balloons out of 5 is given by “5 Choose 3”: 5! / 2! * 3! = 10 different possible sets.
*We are effectively dividing the 5 balloons into a “Yes” pool and a “No” pool.

Question 292

WORD PROBLEMS
“Joe will pick 3 friends to join him on a road trip. Among his friends are 4 musicians and 3 poets. In how many different ways can Joe select his 3 traveling companions so that he has at least one musician and at least one poet among them?”.

Answer 292

30
1. Tengo que considerar cada caso posible: Joe tendría que seleccionar ya sea dos musicos y un poeta, o bien, dos poetas y un musico.
2. Realizar la división de factoriales por cada caso posible del problema. El número de maneras Joe puede seleccionar 2 músicos de entre 4 opciones, es: 4! / 2! * 2! = 24 / 6 = 4.
3. Posteriormente, se debe calcular el número de maneras para seleccionar 1 poeta de entre 3 poetas: 3.
Entonces, 6 x 3 = 18

Question 293

WORD PROBLEMS
“Towns X and Y are 220 miles apart along a road. Car A, traveling at 20 miles per hour, leaves from Town X towards Town Y at the same time as Car B, traveling at 35 miles per hour, leaves Town Y towards Town X. How many miles will Car B have traveled when the two cars pass by each other?”.

Answer 293

140
RTD Chart
Car R (Miles / Hour) T (Hours) D (Miles)
A 20 t 20t
B 35 t 35t
The Times for the two cars are equal, because they start simultaneously. The sum of the distances traveled by the two cars must equal 220 miles. We can solve for “t” from 20t + 35t = 55t = 220, yielding “t” = 4 hours. The Distance traveled by Car B is then found as follows:
R x t = 35 x 4 = 140 miles.

Question 294

WORD PROBLEMS
“The average weight of men in a meeting room is 170 pounds, and the average weight of the woman is 130 pounds. If more than 60% of the people in the room are men, which of the following could be the average weight of all the people on the room?”.
Select all choices that apply:
a) 144 b) 148 c) 150 d) 152 e) 154 f) 156 g) 158 h) 168

Answer 294

F, G, H
This problem can be solved as a Weighted Average Problem. The overall average weight will be between 130 and 170 pounds, but closer to 170 pounds because there are more men than women in the room. We can use the limiting percentage of 60 to establish the lower bound on the overall average weight.
The “weights” to use in the Weighted Average Formula are 60% or 3/5 for the men, and 40% or 2/5 for the woman. The lower bound on the average weight is thus: [3/5 * 170] + [2/5 * 130] = 102 + 52 = 154 pounds. 154 is NOT possible, because the percentage of men is greater than 60; however all the values higher than 154 are possible.

Question 295

WORD PROBLEMS
“Two Journalists have 8 hours in which to copy-edit a total of 100 articles. If Journalist A copy-edits at a steady rate of 3.5 articles per hour, how many articles per hour must Journalist B copy-edit in order to complete the assignment on time?”.

Answer 295

9
Formula: W = RT —> 3.5 articles per hour x 8 hours = 28 articles. Journalist B must therefore copy-edit 100-28 = 72 articles.
To find Journalist B’s rate, we simply plug 72 for Work into the Work formula and solve for B’s rate. R x 8 hours = 72, so R = 9 articles per hour.

Question 296

WORD PROBLEMS
“The ratio of Boys to Girls in a certain school is greater than 1. When 2 Boys leave and 3 Girls are added to the school, the ratio still favors Boys. What is the least number of Boys that could have been originally enrolled in the school, assuming there was originally AT LEAST one Girls?”.

Answer 296

7
Because the ratio of Boys to Girls is greater than 1, we know there are more Boys than Girls in the school: B > G.
When 2 Boys leave and 3 Girls are added the ratio is still greater than 1, so we can say: B - 2 / G + 3 > 1.
Solving: B - 2 > G + 3 —> B > G + 5
Thus, we choose G to yield B > 6
Therefore, the least number of Boys that could have been originally enrolled in the school is 7.

Question 297

WORD PROBLEMS
“If 40% of the attendees at an event are over 50 years old, and another 20% are under 20 years old. What percent of the attendees are between 20 and 50 years old?”.

Answer 297

40%
Se establece el 100% y a partir de ahí empiezo a restar:
100% - 40% - 20% = 40%

Question 298

PROBABILITY
“The probability of rainfall in City X on any given day is 30%. The probability of rainfall on any given day is independent of whether it rains on any other day.
A) What is the probability of rainfall in City X on AT LEAST one day out of two days.
B) What is the probability of no rainfall in City X on either of those two days”.

Answer 298

A) 0.51 or 51%
The probability of rainfall on at least one of the two days is equal to:
P(Rain 1st Day) + P(Rain 2nd Day) - P(Rain Both Days), since rainfall on each day is independent of what happened on other days. This probability equals 0.3 + 0.3 - (0.3 x 0.3) = 0.6 - 0.09 = 0.51 or 51%
Alternatively, we can use the “1 - x” trick here: the probability of rainfall on at least one of the two days is 1 - the probability of rain on neither day = 1 - 0.7 x 0.7 = 1 - 0.49 = 0.51 = 51%
B) The probability of no rainfall on either day, follows from the work above: 0.7 x 0.7 = 0.49 or 49%

B)

Question 299

SKILL

¿Cuántos Centavos hay en $1 Dólar?

Answer 299

100 Centavos

Question 300

WORD PROBLEMS
“Jennifer can purchase 11-Cent and 21-Cent stamps. If she intends to spend EXACTLY $2.84 on these stamps, which of the following is a possible number of 11-Cent stamps she can purchase?”.
A) 0 B) 1 C) 2 D) 3 E) 4

Answer 300

B = 1
La opción es probar cada opción que me dan.
Como tengo $2.84 dólares para gastar y “compro” 1 estama de 11 Centavos, resto $2.84 - 0.11 (porque son Centavos) =
$2.84 - $0.11 = $2.73.
Posteriormente, divido $2.73 / $0.21 = 13. Como 13 es la úniva división que resulta en entero, esa es la correcta.

Question 301

“Each employee of a certain company is in either Department X or Department Y, and there are more than twice as many employees in Department X as in Department Y. The Average (Arithmetic Mean) salary is $25,000 for the employees in Department X and $35,000 for the employees in Department Y. Which of the following amounts could be the average salary for all the employees of the company”.
A) $26,000 B) 28,000 C) 29,000 D) 30,000

Answer 301

A, B
Una estrategia es irme al extremo con la información que me han dado: “… there are more than twice as many employees in Department X as in Department Y”.
-Mínimo es el doble-, entonces multiplico $25,000 por 2 y $35,000 por 1:
50,000 + 35,000
——————– = 28,333.
2 + 1 = 3
Entonces, las respuesta correcta tiene que ser menor a 28,333: letras A y B.

Question 302

WEIGHTED AVERAGES
“On a ferry, there are 50 cars and 10 trucks. The cars have an average mass of 1,200 KG and the trucks have an average mass of 3,000 KG.
What is the Average mass of all 60 vehicles on the ferry?”.

Answer 302

1,500
Primero debo conseguir la suma de los KG tanto de los carros como de los Trucks:
Carros: 50*1,200 = 60,000 KG
Trucks: 10*3,000 = 30,000 KG
Posteriormente, obtengo el promedio de ambos números, sumándolos y dividiéndolos entre el número total de autos:
90,000
-------- = 1,500
60

Question 303

WEIGHTED AVERAGE
“In a certain company, 70% of employees are marketers who make an average of $40,000; 20% are programmers who make an average of $80,000; and 10% are managers, who make an average of $120,000. What is the average salary of all employees at this company?”.

Answer 303

$56,000
7 1 1
— $40,000 + — $80,000 + — $120,000 =
10 5 10

28,000 + 16,000 + 12,000 = 56,000

Question 304

SKILL:

What is 46.7 rounded to the nearest integer?

Answer 304

47

Question 305

SKILL:
Rectangle R has a perimeter of 80. The square S has a perimeter of 20.
The perimeter of S is what fraction of the perimeter of R?

Answer 305

20 1
— = —
80 4

Question 306

WORD PROBLEMS
“Working alone at its constant Rate, Machine A produces “k” liters of a chemical in 10 minutes. Working alone at its constant Rate, machine B produces “k” liters of the chemical in 15 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant Rates, to produce “k” liters of the chemical?”.

Answer 306

6 minutes.
When the machines work simultaneously, the Rate at which the chemical is produced is the sum of these two Rates.
K K 15K + 10K 25K K
——— + ——– = —————- = ———— = —
10 min 15 min 150 min 150 min 6
To compute the Time r equired to produce “k” liters at the Rate K/6, divide the amount “k” by the Rate k/6 to get k/1 / k/6 = 6

Question 307

SKILL

1.0869565 rounded to the nearest 0.1%?

Answer 307

108.7%
1.0869565 x 100 = 108.69565
Rounded = 108.7%

Question 308

SKILL

What is 10.49 rounded to the nearest tenth?

Answer 308

10. 5
11. We identify the number placed in the “tenths” position: 4
12. We look to the number located to the right of 4, in this case 9
13. Is 9 greater or equal to 5? If yes, the 4 adds 1 to become 5.
14. Result: 10.5

Question 309

SKILL

What is the multiplier of a 17.6% increase?

Answer 309

1.176

Question 310

SKILL

Round to the nearest 0.01 the number: 57.939624

Answer 310

57.94

Question 311

SKILL

1 Mile equals how many Feet?

Answer 311

1 Mile = 5,280 Feet

Question 312

“The average (arithmetic mean) of 100 measurements is 23, and the average of 50 additional measurements is 27. What is the average of the 150 measurements?”.

Answer 312

4.333
The Average of all 150 measurements would be the sum of all values divided by 150.
100 measurements x 23 = 2,300
50 additional measurements x 27 = 1,350
2,300 + 1,350
----------------- = 24.333
150

Question 313

“One of the roots of the equation x^2 + kx - 6 = 0, is 3; and k is a constant.
The question is: What quantity is bigger: k or -1?”.

Answer 313

Both quantities are equal.
If I have been given one of the roots of a quadratic equation, in this case 3, it means that when “x” is 3, the equation is correctly satisfied.
So what I have to do is to solve for “k” and compare its value with -1:
3^2 + k(3) - 6 = 0
“k” = -1
So both quantities are equal.

Question 314

What is the Probability of an outcome?

Answer 314

Total outcomes

Question 315

SKILL

If the problem says the word “approximately”, remember:

Answer 315

El resultado que obtenga de mis cálculos, NO necesariamente tiene que aparecer como una opción de respuesta. Si este es el caso, la respuesta correcta es el número que más se acerque a la respuesta que yo obtuve.

Question 316

If the Diameter of Circle “C” is 3 times the Diameter of Circle “D”, then the area of Circle “C” is how many times the area of Circle “D”?

Answer 316

9
Circle “C” Circle “D”
3d d
Because Diameter and radius are directly related, if the radius of Circle “D” is “r”, then the radius of Circle “C” is 3r.
The area of Circle “C”: PI(3r)^2
—————— = 9
The area of Circle “D”: PI(r)^2

Question 317

Last year Kate spent between 1/4 and 1/3 of her gross income on her mortgage payments. If Kate spent $13,470 on her mortgage payments last year, which of the following could have been her gross income last year?
Indicate ALL such gross incomes:
A) $40,200
B) $43,350
C) $47,256
D) $51,996
E) $53,808

Answer 317

B, C, D y E
El secreto está en utilizar ambas fracciones del “gross income X”, 1/4 y 1/3, igual a $13,470.
1/4x = $13,470 = 53,880
1/3x = $13,470 = 40,410
El rango de posibles cantitades de “gross income”, va a partir de 40,410 hasta 53,880: B, C, D y E.

Question 318

GEOMETRY

En problemas de trángulos recuerda que aunque no me den las medidas del área, y ésta esté dividida en partes iguales…

Answer 318

Debo considerar la opción de que ambas porciones de un trángulo que está dividido en dos (las bases son iguales), tendrían la misma área.

Question 319

SKILL: PARA ENCONTRAR LA “MEDIAN” DE UN GRUPO DE DATOS…

Answer 319

Debo ordenar los números “from least to greatest”.

Question 320

In the expression 
3s + 4
---------
     3
Can I cancel out the 3 with the "3s"?

Answer 320

No, because there is a “plus - addition” sign.
We actually have to divide each term by 3:
s + 4/3

Question 321

How many 2-digit positive integers are there such that the product of their two digits is 24?

Answer 321

Four.
En preguntas de este tipo tengo aue enlistar todos los factores de 24:
1 * 24 = 24 —–> Eliminado porque es un “2-digit” number.
2 * 12 = 24 —–> Eliminado porque es un “2-digit” number.
3 * 8 = 24 —–> Sí aplica y como dos números diferentes: 38 y 83
4 * 6 = 24 —–> Sí aplica y como dos números diferentes: 46 y 64

Question 322

At a certain fruit stand, the price of an apple is twice the price of an orange. For which of the following combinations of apples and oranges is the total price equal to the total price of 20 oranges?
Indicate ALL such combinations:
a) 2 apples and 16 oranges.
b) 3 apples and 14 oranges.
c) 4 apples and 10 oranges
d) 6 apples and 8 oranges.

Answer 322

A, B, D.
El secreto está en probar cada una de las respuestas.
Orange = x
Apple = 2x
La respuesta correcta debe resultar en el precio total de veinte naranjas = 20x
a) 4x + 16x = 20x —–> Aplica como respuesta correcta.
b) 6x + 14x = 20x —–> Aplica como respuesta correcta.
c) 8x + 10x = 18x —–> No aplica como respuesta correcta.
d) 12x + 8x = 20x —–> Aplica como respuesta correcta.

Question 323

A third-grade teacher has “n” boxes, each containing 12 pencils. After the teacher gives “p” pencils to each student in the class, the teacher has “t” pencils left over. Which of the following represents the number of students in the class?

a) 12n-t/p
b) 12n+t/p

Answer 323

A.
Secreto 1: No quedarme sólo con las variables que tengo en el problema. En este caso, si me piden la expresión que represente el número de estudiantes de la clase, debo incluir una variable adicional para obtenerlo, por ejemplo: “x”. Entonces el Maestro dio a sus estudiantes, “px” pencils.
Entonces, si sabemos que el maestro tiene “12n” cajas de lápices y regaló “px” = 12n - px = t —–> Then solve for “x”= 12n-t/p

Question 324

If “x”> 0, then

(Square Root of 4x + Square Root of 9x) ^2 =

Answer 324

25x
El secreto inicial es simplificar una raíz cuadrada a la vez:
Square Root of 4x = 2Raíz Cuadrada de “x”
Square Root of 9x = 3Raíz Cuadrada de “x”
Entonces tenemos la siguiente expresión:
(2Raíz Cuadrada de “x” + 3Raíz Cuadrada de “x”)^2
Ataco el paréntesis y luego elevo al cuadrado^2:
(Raíz Cuadrada de 5x)^2 = 25x

Question 325

Which of the following points are on the graphs of both the equation
y = x + 2, and the equation y = x^2.

Answer 325

Se contesta como una "quadratic equation".
x^2 = x + 2
x^2 - x - 2 = 0
(x - 2) (x +1) = 0
x = 2, -1
Finalmente, sustituyo los dos valores de "x" que conseguí, en la expresión original, y = x + 2. 
y = 4
y = 1
Los puntos finales, son: (2,4) y (-1,1)

Question 326

COORDINATE GEOMETRY
Recuerda que entre dos líneas, aunque no tenga sus puntos en el plano carteciano, puedo saber cuál que “Slope”, es más grande.

Answer 326

The line that rises faster (or is steeper), es la que tiene una “greater slope”.

Question 327

Machine R, working alone at a constant Rate, produces “x” units of a product in 30 minutes, and Machine S, working alone at a constant Rate, produces “x” units of the product in 48 minutes, where “x” is a positive integer. What is the number of units of the product that Machine R, working alone at its constant Rate, produces in 3 hours.

Answer 327

6x
El secreto es la multiplicación de la proporción x/30 minutos, "por" los minutos solicitados por el problema: en este caso, 3 horas = 
180 minutos.
        x
------------- * 3 * 60 = 6x
30 minutes

Question 328

GEOMETRY
Si estoy trabajando con un Cuadrilátero inscrito dentro de un Círculo, del cual solo conozco su Diámetro: por ejemplo 10, y que no forma parte del Cuadrilátero (el diámetro), debo recordar:

Answer 328

Que es probable que no tenga suficiente información para calcular el Área de dicho Cuadrilátero. No puedo asumir la posición de cada uno de los puntos que lo conforman (al Cuadrilátero).

Question 329

COORDINATE GEOMETRY

Para encontrar valores de Funciones, llamadas en inglés “Functions f”, debo recordar:

Answer 329

Que debo ubicar en el Plano Cartesiano los “puntos” que indica el problema. El dato numérico que acompaña a la Función es una coordenada que se sitúa en el eje de la “x”.

Question 330

Of the 700 members of a certain organization, 120 are Lawyers. Two members of the organization will be selected at random. Which of the following is closest to the probability that neither of the members selected will be a Lawyer?

Answer 330

Aproximádamente, 0.7.
El secreto está en la doble división de las siguientes cantidades:
1. De mi universo de “No Abogados”, que es de 580 personas, tengo que seleccionar a 2 = 580!/2!*578! Este dato es el numerador de la proporción que necesito.
2. El denominador de la proporción que necesito, viene de las 2 personas que selecciono de entre el universo total de Miembros de la Organización: 700!/2!698!
Entonces, mi resultado final es: 0.68, ó aproximadamente 0.7

Question 331

COORDINATE GEOMETRY

Cuál es el punto medio del segmento de una línea cuyos puntos finales son: (2,9) y (2,0).

Answer 331

(2, 4.5), o bien, (2, 9/2)
Solo necesito obtener el promedio de los dos valores de “x” y el promedio de los dos valores de “y”.
2+2/2 = 2
9+0/2 = 4.5

Question 332

COORDINATE PLANE
Line “k” lies in the xy-plane. The x-intercept of line “k” is -4, and line “k” passes through the midpoint of the line segment whose endpoints are (2,9) and (2,0). What is the slope of the line “k”?

Answer 332

3/4
1. Obtengo el punto medio de las coordenadas (2,9) y (2,0).
2+2/2 = 2
9+0/2 = 4.5 ó simplemente 9/2.
2. Si x-intercept es -4, entonces puedo asignar a “y”, el valor de 0.
3. Encontrar la “Slope”, por medio de la formula:
“Y”dos - “Y”uno / “X”dos - “X”uno
9/2 - 0 / 2 - (-4) = 3/4

Question 333

AREA OF A PARALLELOGRAM

Answer 333

Area = Base * Height

Question 334

GEOMETRY

Para calcular el área de un Paralelogramo (Parallelogram), debo considerar:

Answer 334

1. La altura se identifica al dibujar una línea “punteada”, recta, desde una de las esquinas de la figura.
2. Esta línea “punteada” formará un triángulo recto.
3. La Hipotenusa de este nuevo triángulo recto, será más grande que sus lados perpendiculares. Con esta información ya puedo estimar una posible área.
4. Si conozco un ángulo, puedo calcular los otros tres: si sé que un ángulo mide 125 grados, su opuesto también medirá 125 grados.
5. Como los ángulos interiores del paralelogramo suman 360 grados, los otros dos ángulos opuestos medirán 55 grados cada uno.

Question 335

CÓMO SUMO LOS ENTEROS DE 1 A “N”

Answer 335

Con la fórmula:
n (n + 1)
———-
2

Question 336

SKILL

RECUERDA QUE CUANDO UNA “INEQUALITY” ES MULTIPLICADA O DIVIDIDA ENTR UN NUMERO NEGATIVO…

Answer 336

LA DIRECCIÓN DE LA “INEQUALITY” CAMBIA.

ESTO ES QUE DEBO CAMBIAR LA DIRECCIÓN DEL SIGNO.

Question 337

If 1 + x + x^2 + x^3 = 60, then the average (arithmetic mean) of x, x^2, x^3, and x^4 is equal to which of the following?
A) 12x
B) 15x
C) 20x

Answer 337

B) 15x
Usualmente, cuando veo potencias de tres o mayores, no tengo que resolver por "x".
x + x^2 + x^3 + x^4
-------------------------
             4
Factorizo, una "x".
x (1 + x + x^2 + x^3)

Question 338

COORDINATE GEOMETRY
Los Paralelogramos (Parallelogram) que "viven" en el Plano Cartesiano, y del cual deseo saber las coordenadas de uno de sus puntos, debo pensar en...

Answer 338

Triángulos Rectos, cuya una de sus esquinas sea el punto que deseo encontrar.
A partir del Paralelogramo, encontraré dos triangulos rectos y las medidas de uno, son exáctamente las medidas del segundo triángulo recto.

Question 339

SKILL

¿El símbolo ‘PI’, se puede elevar al cuadrado?

Answer 339

Sí. Es legar indicar una potencia al símbolo que representa “PI”.

Question 340

What is 22/17 to the nearest 0.01?

Answer 340

1.29

The complete quotient is: 1.29411765

Question 341

¿Cómo calcular el ratio aproximado de la siguiente proporción?

34

Opciones de respuesta:
A) 8 to 1
B) 10 to 1

Answer 341

Multiplicando.
Pruebo cada una de las opciones de respuesta que me dan y veo cuál es la más cercana (porque en la pregunta me piden “aproximado”).
A) 8 to 1 —> Multiplico 8 * 34 = 272
B) 10 to 1 —> Multiplico 10 * 34 = 340
272 es más cercano al numerador de la proporción y por ello es la respuesta correcta.

Question 342

SKILL

Recuerda que el lado opuesto al mayor ángulo de un triángulo…

Answer 342

Es el lado más largo.

Por el contrario, el lado opuesto a un ángulo menor, tendrá una longitud menor.

Question 343

Si x > y, ¿qué puedo decir de x/y?

Answer 343

Que

x
— > 1
y

Question 344

“p” is the probability that event “E” will occur; and “s” is the probability that event “E” will not occur.
Which quantity is bigger:
A) p + s
B) ps

Answer 344

A) p + s
“p + s” siempre será igual a 1. Es decir, “p” y “s” son decimales entre 0 y 1.
Entonces, “s” = 1-p

B) “ps” = p (1-p) = p-p^2
Basta con sustituir posibles valores para “p” (que caigan dentro del rango 0-1), para confirmar que p-p^2 es igual a una cantidad menor a 1. Por ello, la opción A) p + s, es la respuesta correcta.

Question 345

STATISTICS
Recuerda que frente a un problema de Standard Deviation, en una distribución normal, el porcentaje de valores se encuentra a dos desviaciones estándar y éstos representan:

Answer 345

El 95% de la información.

Question 346

The total amount that Mary paid for a book was equal to the price of the book plus a sales tax that was 4% of the price of the book. Mary paid for the book with a $10 bill and received the correct change, which was less than $3.
Which of the following statements must be true?
A) The price of the book was less than $9.50
B) The price of the book was greater than $6.90
C) the sales tax was less than $0.45

Answer 346

C
Secreto: Si detecto rangos en precios, vale la pena considerar “inequalities”.
P = Price of the book + 0.04% de tax = 1.04p
Como recibo menos de $3 de cambio = $7

Question 347

In range of prices problems, remember:

Answer 347

To test “extremes values”. This way I will know the extreme range of possible values, the cheaper and the most expensive.

Question 348

If x > 1, which quantity is bigger?
x -x
A) ——— B) ———
x +1 1 - x

Answer 348

B)
Primero, hacemos de la expresión “B” una más sencilla, convirtiendo las variables negativas, en positivas, multiplicando numerador y denominador por -1.
1
———
x - 1
Con esta información ya podemos “ver” que A) es más pequeña, porque el numerador es igual en ambos casos y la comparación recae en el demominador.
La cantidad A) es más pequeña porque estamos dividiendo entre un número más grande.

Question 349

COORDINATE GEOMETRY
Recuerda que para saber la Slope de una línea, a fin de compararla con otra Slope de otra línea (ambas situadas en el mismo plano cartesiano), necesito:

Answer 349

Dos puntos por línea, de tal forma que no se pueda mover su Slope y con ello tener solo una Slope por cada línea.

Question 350

Cuando trabaje con “inequalities” en fracción, debo recordar que solo puedo hacer una cross-multiplication para aislar una variable, siempre y cuando…

Answer 350

Todos los términos de la inequalidad sean positivos.

Question 351

Points W, X, Y y Z are on a line, not necessarily in that order. The distance between W and X is 2, the distance between X and Y is 4, and the distance between Y and Z is 9. Which of the following could be the distance between X and Z?
A) 3
B) 5
C) 7

Answer 351

B) 5
En este tipo de ejercicios tengo que buscar acomodar las variables en distintas formas hasta dar con el resultado. El exámen sabe que yo las acomodaré (las variables) en orden (W,X,Y,Z)
y de esa forma no llegaré a la respuesta correcta.
Las líneas las acomodo en bloques, una debajo de la otra.

Question 352

COMBINATORICS
Un problema de combinación, por ejemplo de dígitos o códigos postales, se resuelve únicamente con multiplicaciones cuando…

Answer 352

… se me permite repetir códigos y dígitos.

Si dos símbolos deben de ser una de las 26 letras de abecedario, solo es cuestión de multiplicar 26*26

Question 353

LEAST COMMON DENOMINATOR
¿Cuál es el Least Common Denominator de las siguientes fracciones?
1/6 + 1/30

Answer 353

1/6 * 1/30 =
Paso 1. Prime Factorization: 1/23 1/235
Paso 1. Me hace falta un 5 en el denominador izquierdo. Entonces multiplico un 5 por el numerador y denominador de la fracción izquierda = 5/23*5
5/30 + 1/30 = 6/30 = 3/15 = 1/5
Otro ejemplo: p + p/2 + p/4 = 1
¿Cuánto es P?
P = 4/7

Question 354

SET A: 0.2, 0.4, 0.6, 0.8
SET B: 2, 4, 6, 8
Which quantity is greater:
A) Standard Deviation of Set A
B) Standard Deviation of Set B

Answer 354

B
For the purpose of the GRE we can think about Standard Deviation as being a measurement of how much the numbers in a set differ from the Mean of that set.
A) Mean of 0.5
B) Mean of 5

Question 355

Andy drove from Townville to Villageton at an average speed of 40 miles per hour. He then drove from Villageton to Townville at an Average Speed of 60 miles per hour. What is the Average Speed of Andy’s entire trip in miles per hour?

Answer 355

48
1. Por cada viaje, debo calcular t = d/s
d/40 + d/60 = 100d/2400 = d/24
2. Con el Tiempo total ya puedo realizar la división:
Total Distance / Total Time: 2d/1 / d/24 = 48

*Como Distancia es “D” la Total Distance es 2D

Question 356

x^4 = y^16, then y =

Answer 356

Fourth Root of "x"
1. Simplificar y^16 a sólo "y".
"Elevo ambos términos a la potencia 1/16
(x^4)^1/16 = (y^16)^1/16
x^1/4 = y^1
y = Fourth Square Root of "x"

Question 357

What is the y-intercept of the graph of the equation y = 2|4x-4| - 10?

Answer 357

-2
The”x” coordinate of any “y” intercept is always equal to zero.
So we need to plug in 0 for “x” and solve for “y”:
y = 2|4(0)-4| - 10?
y = 2(4)-10 = -2

Question 358

What is greater 0.24 or 0.2?

Answer 358

0.24

Question 359

8.0 is approximately what percent of 5.1?

A) 40%
B) 57%
C) 64%

Answer 359

B) 57%
We first find the difference:
8.0 - 5.1 = 2.9
2.9
----- * 100 = 58

Question 360

What is the number of integers between 100 and 500 that are multiples of 11?

Answer 360

36

1. Primer múltiplo de 11, después de 100: 11*10 = 110
2. Último múltiplo de 11, antes de 500: 11*45 = 495
3. Resta. Último múltiplo - Primer múltiplo = 385
4. 385/11 = 35
5. 35+1= 36

Question 361

In a regular 9-sided polygon, what is the value of each angle?

Answer 361

140
(n-2) * 180 = 7*180 = 1,260
Finally, in order to get each angle measurement I have to divide by the number of sides: 1,260/9 = 140

Question 362

The function "f" is defined for all numbers "x" by f(x) = x^2 + x. If "t" is a number such that f(2t) = 30, which two of the following could be the number "t"?
A) -5
B) -3
C) -1/2
D) 2
E) 5/2

Answer 362

B) -3 E) 5/2
1. Reemplazo “x” por “2t” = (2t)^2 + 2t = 30
2. En este caso, también puedo considerar x^2 + x = 30
3. x^2 + x - 30 = 0
4. (x + 6) (x - 5) = -6, 5
5. Reemplazo “x” por “2t” —> 2t = -6 2t = 5
t = -3 t = 5/2

Question 363

8.0 is approximately what percent of 5.1?

A) 40%
B) 57%
C) 64%

Answer 363

B) 57%
We first find the difference:
8.0 - 5.1 = 2.9
2.9
----- * 100 = 58

Question 364

What is the number of integers between 100 and 500 that are multiples of 11?

Answer 364

36

1. Primer múltiplo de 11, después de 100: 11*10 = 110
2. Último múltiplo de 11, antes de 500: 11*45 = 495
3. Resta. Último múltiplo - Primer múltiplo = 385
4. 385/11 = 35
5. 35+1= 36

Question 365

8.0 is approximately what percent of 5.1?

A) 40%
B) 57%
C) 64%

Answer 365

B) 57%
We first find the difference:
8.0 - 5.1 = 2.9
2.9
----- * 100 = 58

Question 366

COORDINATE PLANE
In the xy-plane, the point (1,2) is on line “j”, and the point (2,1) is on line “k”. Each of the lines has a positive slope.
Which quantity is greater:

A) The slope of line “j”

B) The slope of line “k”

Answer 366

The relationship cannot be determined from the information given.
Porque solo tengo un punto de la línea, lo cual permite que “juegue” con la pendiente como yo quiera.

Question 367

A certain identification code is a list of five symbols: SSDDD. Each of the first 2 symbols must be one of the 26 letters of the English alphabet, and each of the last 3 symbols must be one of the 10 digits. (Repeated letters and digits are allowed).
What is the total number of different identification codes?

Answer 367

676,000
Como la repetición de números y letras está permitida:
26 x 26 x 10 x 10 x 10 = 676,000

Question 368

PROBABILITY

¿Qué significa que los experimeitos en una probabilidad son “mutually exclusive”?

Answer 368

Que una probabilidad no depende de la otra para suceder. Son independientes.
Por ejemplo: “A certain experiment has three possible outcomes. The lutcomes are “mutually exclusive” and have probabilities “p”, “p/2”, and “p/4”, respectively. What is the value of “p”?
Respuesta: p + p/2 + p/4 = 1

Question 369

ODD + ODD =

Answer 369

EVEN

Question 370

ODD - ODD =

Answer 370

EVEN

Question 371

ODD + EVEN =

Answer 371

ODD

Question 372

ODD - EVEN =

Answer 372

ODD

Question 373

ODD * ODD =

Answer 373

ODD

Question 374

ODD * EVEN =

Answer 374

EVEN

Question 375

EVEN * EVEN =

Answer 375

EVEN

Question 376

In the first half of the year, a team won 60 percent of the games it played. In the second half of last year, the team played 20 games, winning 3 of them. If the team won 50 percent of the games it played last year, what was the total number of games the team played last year.

Answer 376

90
El secreto está en establecer a “x” como el número de juegos jugados durante el primer semestre, de tal forma que el total anual es:
x + 20 = ?
Entonces, la relación de planteamientos matemáticos se establece por medio de los juegos ganados.
0.60x + 3 = 0.50 (x + 20)
x = 70
70 + 20 = 90

1st half of the year: 60% games won.
2nd half of the year: 20 games. 3 won, 17 lost.

Question 377

GEOMETRY

The Perimeter of Square “S” is 40. Square “T” is inscribed in square “S”. What is the least possible area of square “T”?

Answer 377

50
1. Reconoce que el Cuadrado “T” se encuentra dentro del Cuadrado “S”, en forma de Rombo, que toca 4 puntos del Cuadrado “S”.
2. Reconoce que el Cuadrado “T” contiene dos triángulos especiales 45-45-90 —> x : x : xSquare Root of 2
3. La Hipotenusa es “xSquare Root of 2” = 10
x = 10 / Square Root of 2
Y como el área de un Cuadrado es Lado^2:
(10 / Square Root of 2)^2 = 100 / 2 = 50

Question 378

A survey asked 1,150 people to choose their favorite laundry detergent from brands A, B and C. Of the people surveyed, "x" percent chose A as their favorite brand. If "x" is rounded to the nearest integer, the result is 3. Which of the following could be the number of people who chose A as their favorite brand?
A) 25
B) 30
C) 35
D) 40
E) 45

Answer 378

B) 30 C) 35 D) 40

1. Identifica el rango de posibles valores de “x” (If “x” is rounded to the nearest integer, the result is 3): 2.5

Question 379

RECUERDA
En problemas de Secuencias (A, Sub 1; A, Sub 2; etc), dadas por una función establecida, como A, Sub k = 1/k - 1/k+1…
me pueden preguntar: “what is the sum of the 100 terms of this sequence”.

Answer 379

Son problemas candidatos a encontrar patrones, por lo que debo encontrar por lo menos los primeros A, Sub 1; A, Sub 2; A, Sub 3; y también dos números antes de llegar a al último número.

Question 380

2^11 * 5^11 =

Answer 380

10^11

Question 381

5^6 * 2^6 =

Answer 381

10^6

Question 382

10^11 * 10^6 =

Answer 382

10^17

Question 383

GEOMETRY

En un problema de Triángulos, recuerda:

Answer 383

Siempre hacer el inventario de lo que tengo, incluyendo encontrar los ángulos internos de los triángulos, ya que ésto me puede ayudar a identificar un triángulo especial 30:60:90 y con ello, sus proporciones.

Question 384

A desert outpost (Avanzada) has a water supply that is sufficient to last 21 days for 15 people. At the same average rate of water consumption per person, how many days would the water supply last for 9 people?

Answer 384

35
1. Asigno una variable a la cantidad de agua que se toma en 21 días: “w”. Entonces w/21
2. La cantidad de agua, w/21, se sabe que es tomada y distribuida entre 15 personas.
Entonces, w/21 / 15/1 —> w/2115 —> w/315, lo cual significa que una persona tendría suficiente agua para 315 días.
3. Nueve personas tendrán suficiente agua por 1/9315 = 35

Question 385

COORDINATE GEOMETRY

The x-intercept of a line given by an equation is the value of “x” when “y” equals 0.

Answer 385

Therefore, the y-intercept of the line is the value of “y” when “x” equals 0.

Question 386

1 - x 1
—— = —
x - 1 x

Quantity A = x
Quantity B = -1/2

Answer 386

Quantity B = -1/2
El secreto está en desaparecer la fracción por medio de cross-multiplication.
x(1-x) = 1(x-1)
x - x^2 = x - 1
Se van las “x”…
-x^2 = -1 —> Multiplico por -1 —> x^2 = 1
Entonces, “x” puede ser 1, o bien, -1 (nota que no se integra ninguna raíz cuadrada como parte del despeje de “x”.
Al sustituir cada uno de los posibles valores de “x” = 1, -1, descubro que “x” es -1, y por lo tanto, más pequeño que -1/2.

Question 387

“WHAT PERCENT GREATER” problem skill…

Answer 387

Primero se realiza la Resta o diferencia de cantidades: Mayor - Menor = Resultado

El Resultado se “divide” entre la cantidad Menor y se multiplica por 100.

Question 388

GEOMETRY
The height of an equilateral triangle with sides of length “r” is:
*r = Radius

Answer 388

Square Root of 3
———————-r
2

Question 389

GEOMETRY

Area of an Equilateral Triangle:

Answer 389

4

*a^2 = Side

Question 390

If a^-1 = 1/a, 1/a^-1 =

Answer 390

a

So, 1/4^-1 = 4

Question 391

EXPONENTS
3^-1
——- =
4^-1

Answer 391

4/3

Question 392

NUMBERS

Which quantity is greater?

A) The sum of the odd integers from 1 to 199.

B) The sum of the even integers from 2 to 198.

Answer 392

A
Sum of terms: (Mean) (Number of Terms)
Mean (or Average) = Sum of Terms / Number of Terms
Mean = Median -> 1 + 199 = 200 —> 200/2 = 100
Number of Terms = 199 - 1 = 198 —> 198/2 = 99 + 1 = 100
Sum of Terms of Quantity A: (100) (100) = 10,000

*I have to do the same for Quantity B (9,900) and compare both.

Question 393

GRAPH
Recuerda que en una gráfica circular / pastel, puedo tener cada “rebanada” dividida en porcentajes. ¿Qué debo responder cuando me preguntan: “In the circle graphs, the degree measure of the central angle of the sector representing the number of workers unemployed for 11 to 14 weeks is how much greater in the Manufacturing industry graph than in the service industry graph?”

Answer 393

Si la rebanada de pastel en cuestión representa, digamos, el 10%, debo de obtener el 10% de 360.
Respuesta Oficial: “Recall that in a Circle Graph the degree measure of the central angle of a Sector representing “n” percent of the Data is equal to “n” percent of 360.

*the degree measure: “la medida en grados”.

Question 394

RATIO
La proporción 2:1.28 es cercana a cuál de las siguientes proporciones:
A) 5 to 4
B) 6 to 5
C) 3 to 2
D) 5 to 2

Answer 394

C) 3 to 2

1. Divido 2/1.28 = 1.5625
2. Divido cada una de las opciones que me dan como opción de respuesta para saber qué resultado es el más cercano a mi primera división.
3. 3/2 = 1.5 y por eso es la respuesta correcta.

Question 395

2/3 is what fraction of its reciprocal?

Answer 395

2
---
3                 4
-------- = --------
3                 9
---
2

Question 396

SCIENTIFIC NOTATION

38300 =

Answer 396

3.83 x 10^4

Question 397

When the positive integer “n” is divided by 3, the reminder is 2 and when “n” is divided by 5, the reminder is 1. What is the least possible value of “n”?

Answer 397

11
El secreto está en recordar que la respuesta correcta debe de ser el primer número común entre la división con 3 y 5.
n/3 = el primer número de la lista es 2 y posteriormente solo sumo 3 a cada término subsecuente, 5, 8, 11, 14…

n/5 = el primer término es 1, y voy sumando 5: 6, 11, 16…
El único número compartido es 11.

Question 398

What is “Nth” term formula?

Answer 398

Nos ayuda a encontrar el número de términos en un Set:
a-Sub n = a + (n-1) * d
Resuelvo por “n”.
d = difference entre los números del Set.

Otra versión de la fórmula: n = aSub”n” - a / d + 1

Question 399

If n^2 = (2^4) (3^4), what would be “n”?

Answer 399

(2^2) (3^2)

Half the exponents.

Question 400

What is the Least Common Multiple of 24 and 108 in Prime Factors?

Answer 400

(2^3) (3^3)

24: (2^3) (3)
108: (2^2) (3^3)
Tomo los exponentes más grandes.

Question 401

Which of the following numbers is NOT the sum of three consecutive odd integers?
A) 15
B) 75
C) 123
D) 297
E) 313

Answer 401

E
El secreto está en reconocer que lo que busco es un NO múltiplo de 3, lo cual podemos saber gracias a un buen planteamiento:
x-2 + x + x+2 = 3x

Question 402

¿Qué significa?
“A tax rate of 5 1/2 dollars per hundred dollars”
“A tax rate of 55 dollars per thousand dollars”
Which tax is greater?

Answer 402

5.5 55
—– and ——
100 1000

Both taxes are equal = 0.055

Question 403

¿Cuánto es, aproximadamente, el 70% de 9 horas 40 minutos?

Answer 403

6 3/4

9 horas 40 minutos = 9 horas y 40/60 = 2/3
9 2/3 = 29 / 3
70/100 * 29/3 =

Question 404

¿Qué cantidad es más grande?

7.9 ó 7.9999

Answer 404

7.9999

Question 405

Which quantity is greater?
A) -2x^2
B) x^2/3
*x is not equal to 0

Answer 405

B) x^2/3
Debo darme cuenta que no importa cuánto valga x, x^2 siempre será positivo, por lo que la expresión completa x^2/3 siempre será positiva.

Por su parte A, -2x^2, es lo mismo que -(2x^2), entonces el término de la expresión dentro del paréntesis siempre será psitivo pero el signo “menos” de afuera la haría negativa.

Question 406

The scale drawing of a certain room is a rectangle 5 inches by 6 inches. If the drawing has the scale 1/4 inch to 1 foot, which of the following will give the actual number of square feet of the room?
A) 90
B) 120
C) 480

Answer 406

C) 480
El secreto es primero realizar la multiplicación que elimine la fracción “1/4 Inch”. Es decir, multiplicar TODO por 4.
4 (1/4) = 4 (1)
1 Inch = 4 Foot
Posteriormente, ya me voy a la figura para multiplicar cada dato INDIVIDUAL “por” 4. 6x4 = 24 5x4 = 20
Finalmente: 24 x 20 = 480

Question 407

Which quantity is greater?
A) 1/0.83
B) 1

Answer 407

A) 1/0.83
El secreto es darme cuenta que la división entre 1 y un número MENOR a 1, resulta en una cantidad mayor a 1, en este caso 1.204.

Question 408

RECUERDA
Cuando un entero se divide entre un decimal, el resultado es un número mayor que el Numerador.
If 0 q

Answer 408

7

• — = 14
  0. 5

Question 409

RECUERDA
Ocasionalmente un problema me pedirá saber cuáles son los números que dividen a un número de “x” cantidad de dígitos.
Un posible planteamiento para un número de 5 dígitos es:

Answer 409

Número = abcde
              = 10,000a + 1,000b + 100c + 10d + e
Número = 38,754
              = 30,000
              = 3 x 10,000 + ...

Question 410

LEAST COMMON MULTIPLE OF:

6 and 8 ?

Answer 410

24

6: 2 x 3
8: 2 x 2 x 2

LCM: 2 x 2 x 2 x 3 = 24

Question 411

The jewels in a crown consist of Diamonds, Rubies, and Emeralds. If the Ratio of Diamonds to Rubies is 5:6 and the Ratio of Rubies to Emeralds is 8:3, what is the least number of jewels that could be in the tiara (ornamental band / high diadem)?

Answer 411

53
El secreto está en obtener el LCM de las cantidades correspondientes a los Rubies 6 y 8:
6: 2 x 3
8: 2 x 2 x 2
LCM: 2 x 2 x 2 x 3 = 24
Diamonds Rubies Emeralds
5 6
8 3
LCM of 6 and 8 = 24
Ahora que sé el LCM, ¿qué sigue?
1. Encontrar el número que al ser multiplicado por 6 (Rubies), resulte en 24, o sea, 4. Dicho número 4, será multiplicado por 5 (Diamonds):
5 x 4 = 20

2. Encontrar el número que al ser multiplicado por 8 (Rubies), resulte en 24, o sea, 3. Dicho número 3, será multiplicado por 3 (Emeralds):
   3 x 3 = 9
   SUMA TOTAL: 20 + 24 + 9 = 53

Question 412

FORMULA FOR SUM OF NATURAL NUMBERS

1,2,3,4,5,6,7,8 …

Answer 412

2

Question 413

Find the sum of even numbers from 1 to 50.

Answer 413

650
Step 1: Total Numbers from 1 to 50 / 2
50/2 = 25
Step 2: (25) (25 + 1) = 650
*Another example:
2 + 4 + 6 + 8 + 10 = n (n + 1) = 5 (6) = 30

Question 414

¿De qué otra forma puedo escribir 72.42?

Answer 414

72 + 42/100

Question 415

PROBABILITY
If one number is chosen at random from the first 1,000 positive integers, what is the probability that the number chosen is a multiple of both 2 and 8?

Answer 415

1/8
Muy importante reconocer que si un número es múltiplo de 8, automáticamente también será múltiplo de 2. Entonces sólo calculo cuántos múltiplos de 8 existen en los primeros 1000 enteros positivos:

Divido: 1000 / 8 = 125

125 1
——– = ——-
1000 8

Question 416

Which of the following is equal to 
1
---(20^8)
4
A) 5^8
B) 4(20^7)
C) 5(20^7)

Answer 416

C) 5(20^7)
El secreto está en desglosar 20^8 y PLANTEAR la división entre 4.
20 x 20 x 20 x 20 x 20 x 20 x 20 x 20
———————————————————–
4
Sólamente uno de los ocho 20 del Numerador se puede “ir” con el 4 del denominador, resultando:
5 x 20 x 20 x 20 x 20 x 20 x 20 x 20, ó bien,
5 (20^7)

Question 417

ALGEBRA
Simplify the following expression:
x^2 - 16        
------------ = 
x - 4

Answer 417

x + 4
El secreto está en reconocer que el numerador es Difference of Squares!
x^2 - 4^2      (x - 4) (x + 4)
------------ = --------------- = x + 4
x - 4              (x - 4)

Question 418

Two cars started from the same point and traveled on a straight course in opposite directions for exactly 2 hours, at which time they were 208 miles apart. If one car traveled, on average, 8 miles per hour faster than the other car, what was the Average Speed of each car for the 2-hour trip?

Answer 418

48 y 56
D = R * T
Car A R 2
Car B R+8 2
2R + 2R + 16 = 208
R = 48
Car A = 48
Car B = 48 + 8 = 56

Question 419

TRANSLATE TO MATH
“A group can charter a particular aircraft at a fixed total cost. If 36 people charter the aircraft rather than 40 people, then the cost per person is greater by $12”.

Answer 419

C = Fixed Total Cost

C C
—– = —– + 12
36 40

C = 4,320

Question 420

FIND THE SLOPE AND y - intercept OF THE LINE WITH EQUATION

2y + x = 6

Answer 420

m (which is the Slope) = -1/2 y-intercept = 3
Debo reescribir la expresión original 2y + x = 6 en la forma
y = mx + b
*m = Slope
*b = y-intercept
A) 2y + x = 6
B) Despejo “y” = 2y = -x + 6 —> y = -x/2 + 3
-x/2 es en realidad -1/2, entonces, “m” es -1/2
C) y-intercept es 3

Question 421

COORDINATE GEOMETRY
Find the equation of the line passing through the point (3,2) with
y-intercept 1

Answer 421

y = 1/3x + 1
Como sé que el y-intercept es 1, puedo inferir que la coordenada total es (0,1).
Ya con los dos puntos puedo hacer la resta
“Diferencia de Y”/”Diferencia de X” = 2-1/3-0 = 1/3

Question 422

COORDINATE GEOMETRY

FIND THE y-intercept OF A LINE WITH SLOPE 3 THAT PASSES THROUGH THE POINT (-2,1)

Answer 422

7
y = 3x + b
I know from the information given in the problem that when "x" is -2, "y" has to be equal to 1.
1 = 3(-2) + b
1 + 6 = b
b = 7

Question 423

COORDINATE PLANE
For the parabola y = x^2 - 4x - 12 in the xy-plane, find the following:

A) The x-intercepts
B) The y-intercept
C) Coordinates of the Vertex

Answer 423

A) Recuerda que “y” sería 0. Posteriormente, resuelvo la Cuadrática:
(x - 6) (x + 2) = 6 y -2. Por lo tanto, ya tengo dos coordenas de la parábola: (6, 0) y (-2, 0).

B) El y-intercept es el punto en el que la parábola toca el Eje de las “y”.
En este caso debo recordar que “x” sería 0, el cual debe ser indicado en la Cuadrática original. y = x^2 - 4x -12 —> y = 0^2 - 4(0) - 12
y = -12. Lo cual me da la coordenada (0, -12)

C) Para encontrar las coordenadas del Vértice, debo encontrar el punto medio entre las dos coordenadas originales (6, 0) y (-2, 0).

• 2 + 6
• ——— = 2

Question 424

INEQUALITY
6x - 5
2 - 5x

Answer 424

El secreto está en reconocer que el signo de “menos” que se encuentra en el término de la derecha, afecta a todo el término, por lo que otra forma de escribirlo sería:
- (6x - 5/3)

3 (2 - 5x)

Question 425

Not Brown Hair: 45
Red Hair: 20
“What fraction of those who do not have Brown Hair, have Red Hair?”

Answer 425

20 4
—— = ——-
45 9
*El 45 es el denominador porque en el problema original es el Total. Es decir, los 20 del numerador formaban parte de los 45.

Question 426

A dealer gives a 25 percent discount on the list price of a radio and still makes a 40 percent profit on the cost of the radio. If the cost of the radio is $30, then the list price of the radio is:

Answer 426

56
"x" = List Price
Profit =  Selling Price - Cost
                .75x - 30 = 0.40 ( 30)
x = 56

Question 427

0

Answer 427

Quantity A: x + x^3 + x^5 + x^7
Factorizando la cantidad “B”, obtengo el mismo bloque de “x” que en “A”.
Quantity A: x + x^3 + x^5 + x^7
Quantity B: x (x + x^3 + x^5 + x^7)
La cantidad A es más grande, dado que estoy trabajando con decimales y esa última multiplicación en realidad haría más pequeña a la cantidad
x + x^3 + x^5 + x^7.

Question 428

Planteamiento de “T is no more than 20 percent greater than the integer “x”

Answer 428

T

Question 429

Planteamiento de “T is no smaller than a number 20 percent less than the integer “x”.

Answer 429

T _> 0.80x

Question 430

GEOMETRY

“Triangles PQR and XYZ are similar. If PQ = 6, PR = 4, and XY = 9, what is the length of side XZ?”

Answer 430

6
La idea es saber que los triángulos similares tienen los mismos ángulos. Por eso a la hora de dibujarlos, las variables de cada vértice deben estar en el mismo orden.
Este problema se resuelve con una proporción:
6 4
—- = —- = Side XZ = 6
9 XZ

Question 431

COORDINATE GEOMETRY
Para identificar líneas paralelas, a partir de ecuacionos como:
y = 2x + 3, tengo que fijarme en:

Answer 431

El Slope de dicha ecuación.
En este caso (y = 2x + 3), tengo una Slope de 2, por lo que una línea paralela también tendría que tener una Slope de 2, por ejemplo:
y = 2x - 5.

Question 432

GEOMETRY

¿Cuál es la proporción de un triángulo especial: 30 : 60 : 90, y cómo está asignada en dicha figura?

Answer 432

x : x Square Root of 3 : 2x

Lado 1 Lado 2 Hipotenusa

Question 433

100
——- =
2 “PI”

Answer 433

“PI”

Question 434

SIMPLIFY
60^2 - PI (30)^2
——————— =
60^2

Answer 434

4

El secreto está en factorizar un 30^2.

Question 435

COORDINATE GEOMETRY
Recuerda que cuando en un problema está involuvrado un Círculo y recibo información como la siguiente: “In the rectangular coordinate system, if (3,1) is a point on circle R and the center of R is (2, -3), what is the Radius of R?

Answer 435

Squar Root of 17.
El secreto está en reconocer que la información “if (3,1) is a point on circle R”, significa que (3,1), en un punto que está en la línea / cuerda del círculo, no en un punto aleatorio del círculo. De esta forma sé que la conexión entre el Centro del círculo y el punto (3,1), es el Radio de la figura.
A partir de ahí trabajo con un triángulo recto en mente para encontrar medidas entre un punto y otro (Hipotenusa).

Question 436

COORDINATE GEOMETRY

Cuál es el área de un tríangulo que se conforma de los puntos: (2,0), (-2,0) y (0, -9/4).

Answer 436

4.5
Base: 4
Height: 9/4  (Para este propósito el signo negativo de la coordenada original -9/4, es irrelevante).
4*9/4
--------- = 4.5
2

Question 437

SIMPLIFICA

(2-x)^2 = 4x^2

Answer 437

Opción 1: 3x^2 + 4x - 4 = 0
Opción 2: Elevar ambos lados de la expresión a una raíz cuadrada. 
2 - x = 2x or - 2x
x = 2\3
x = -2

Question 438

COORDINATE GEOMETRY
For the line with equation y = ax + b (ab is not zero), the x-intercept is twice the y-intercept.

Column A: The Slope of the line
Column B: 1/2

Answer 438

Column B: 1/2

1. Pienso en la fórmula: y = ax + b
2. y-intercept = b
3. x-intercept = 2b
4. Llamemos a x-intercept “C”. y-intercept sería 0
   
   • -> Coordenada (C,0)
5. 0 = aC + b
6. C = -b/a
7. -b/a = 2b
8. -b = 2ab
9. Divido ambos lados por “b”, para desaparecer convertir el lado izquierdo en -1.
10. -1 = 2a
11. a = -1/2
12. -1/2

Question 439

DATA ANALYSIS
¿Cómo calculo el ángulo de una sección determinada en una gráfica de pastel, cuya rebanada representa 20% del total de datos de dicha gráfica?

Answer 439

20% of 360 grados = 72 grados.

Question 440

DATA ANALYSIS

¿Qué significa tener un set con una Standard Deviation de cero?

Answer 440

Que todos los números del set son idénticos.

Question 441

PERMUTATION

In a Permutation problem:

Answer 441

I just do the multiplication, NO DIVISION.

8 x 7 x 6 …

Question 442

COMBINATION

In a Combination problem…

Answer 442

I do multiplication and division.
8 x 7 x 6
————-
1 x 2 x 3

Question 443

STATISTICS
The Standard Deviation of the nine numbers Set: 19, 21, 22, 22, 28, 31, 33, 44, 50, is approximately equal to 10.2
Find the Interquartile Range of the 9 numbers.

Answer 443

1. Identify Second Quartile (Median) = 28
2. First Quartile is the Median of the first half of the Set: 19, 21, 22, 22 = 21.5
3. Third Quartile is the Median of the last half of the Set: 31, 33, 44, 50 = 38.5
   The Interquartile Range = Third Quartile - First Quartile =
   38.5 - 21.5 = 17

Question 444

STATISTICS

Recuerda que cuando se resta cierto número a cada elemento de un set, ¿qué le sucede a la Desviación Estándar original?

Answer 444

Nada, se queda igual, porque es resta.

Sólo cambia la Desviación Estándar cuando se MULTIPLICA cada elemento del Set por otro número.

Question 445

STATISTICS
A group of 20 values has a Mean of 85 and a Median of 80. A different group of 30 values has a mean of 75 and a Median of 72.

A) What is the Mean of the 50 values?
B) What is the Median of the 50 values?

Answer 445

A) Debo saber la suma de los números en cada Set y dividirla entre 50.
20 x 85 + 30 x 75 3,950
————————– = ————– = 79
20 + 30 50

B) Sólo porque tenemos el dato de las dos Medians de cada set, no significa que en este caso tenga suficiente información para obtenerla. No tengo el ranking de cada número.
No tengo suficiente información para obtener la Median.

Question 446

STATISTICS
Find the Mean and Median of the values of the random variable X, whose relative frequency distribution is given in the table below.
X         Relative Frequency
-----------------------------------
0          0.18
1          0.33
2          0.10
3          0.06
4          0.33

Answer 446

Mean:
1. Multiplico cada número de la lista Random Variable X “por” el número que le corresponde a la derecha, en la lista Relative Frequency.
Sumo los resultados y el número final es la Mean.
(0 x 0.18) + (1 x 0.33) + (2 x 0.10) + (3 x 0.06) + (4 x 0.33) = 2.03

Median:
En problemas de Frecuencia debo buscar el valor donde cae el 0.5. Para conseguirlo debo sumar (a partir de cualquier dirección) hasta llegar a dicho valor.
Si empiezo a sumar del 0.18 + 0.33 = 0.51. Por ello, la Median es 1 (en número a la izquierda de 0.33.

Question 447

Martha invited 4 friends to go with her to the movies. There are 120 different ways in which they can sit together in a row of 5 seats, one person per seat. In how many of those ways is Martha sitting in the middle seat?

Answer 447

24
El 120 viene de la cantidad de personas en las que podemos sentar a cinco personas en una fila de 5 asientos: 5! = 120
La posición de Martha siempre será la misma, por lo que solo me quedan 4 lugares para sentar al resto de sus 4 amigos.
M
—– —– —– —– —–
4 x 3 x 2 x 1 = 4! = 24

Question 448

How many 3-digit positive integers are odd and do not contain the digit 5?

Answer 448

288
Enlisto todos los números que puedo utilizar para armar el número de tres dígitos.
0, 1, 2, 3, 4, X, 6, 7, 8, 9
Ahora debo colocar en cada espacio, la cantidad de números que podría utilizar para armar el 3-digit number:
*el zero no puede estar en la posición de las centenas, por ello en dicha posición sólo tengo 8 opciones.
En la segunda posición ya juega el 0 y en la tercera, como el 3-digit number es “odd”, solo tengo cuatro opciones (1, 3, 7, 9).
8 x 9 x 4
—– —– —– = 288

Question 449

From a box of 10 lightbulbs, you are to remove 4. How many different sets of 4 lightbulbs could you remove?

Answer 449

210
Es un problema de "Combination" porque el orden no importa.
El planteamiento es: 10C4 (10 chose 4).
10!
-------- = 210
6! 4!

Question 450

A talent contest has 8 contestants. Judges must award prizes for first, second, and third places, with no ties.
A) In how many different ways can the judges award the 3 prizes?
B) How many different groups of 3 people can get prizes?

Answer 450

A) 8 x 7 x 6 = 336

B) Combination Question: 8C3 =

8!
—– = 56
5! 3!

Question 451

PROBABILIDAD

En el planteamiento P (A or B) = P (A) + P (B) - P (A and B)

Answer 451

P (A) + P (B) - P (A and B)
*Si el problema me dice que los eventos en cuestión son “Mutually Exclusive”, significa que no pueden ocurrir al mismo tiempo. Por ello, en tal caso, la probabilidad, P (A and B), es 0.

Question 452

PROBABILIDAD

Recuerda que en un par eventos P (C and D) “Independent”, es:

Answer 452

La probabilidad de los eventos individuales multiplicados.

P (C and D) = P (C) * P (D)

Question 453

Of the 700 members of a certain organization, 120 are lawyers. Two members of the organization will be selected at random. Which of the following is closest to the probability that NEITHER of the members selected will be a lawyer?
A) 0.5
B) 0.6
C) 0.7

Answer 453

C) 0.7
Primero tengo que saber que dos miembros del grupo de 580 personas que NO son abogados, serán seleccionados.
580C2 =
580 x 579
--------------- = 167,910
     2!
Posteriormente, divido entre el número de formas que hay para seleccionar a dos personas de entre un grupo de 700 personas.
700C2 
700 x 699
-------------- = 244,650
    2!
167,910
------------ = 0.68
244,650
0.68 --> C) 0.7

Question 454

PERCENT INCREASE

What is the percent increase from 4,500 sales in cars to 7,000 sales in cars?

Answer 454

55%

7,000 - 4,500 = 2,500

2,500
——————- * 100 = 55%
4,500 (original starting point)

Question 455

SCIENTIFIC NOTATION

20,000,000,000 =

100,000 =

Answer 455

20,000,000,000 = 20 x 10^9

100,000 = 10^5

*Si los quiero dividir:
20 x 10^9
————— = 20 x 10^4 = 200,000
10^5

Question 456

STATISTICS
If "d" is the Standard Deviation of the numbers in the list above, for which of the following values of "x" would the value of "d" be least?
A) 0
B) 5
C) 20
D) 30
E) 80

Answer 456

C) 20
10, 15, 25, 30, x
Poner atención en los números que sé y sacar su promedio:
10 + 15 + 25 + 30
———————- = 20
4
El numero que va a “deviate the least”, es el número más cercano o igual al Average (20) de los números que conozco.
De esta forma si “x” es 20, la desviación estándar va a contribuir menos a la desviación estándar.