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MANHATTAN GRE Flashcards

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1
Q

GRE CODE

“What is the greatest integer value of “n” such that 2^n is a factor…”

A

Lo que me preguntan es: “How many 2’s go in…”

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2
Q

GRE CODE

An integer “x” has no factor “m” such that 1

A

Significa: “x” is prime.

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3
Q

GRE CODE

Si el problema me pregunta por el “greatest integer less than”, es muy probable que la respuesta sea:

A

Un número primo.

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4
Q

WHICH QUANTITY IS GREATER:
A) 200^5 40^10
B) 8000^15

A

B) 8000^15
El secreto está en descomponer 8000^15, en: 8000^5 8000^10.
Posteriormente, comparar: (Smaller) 200^5 VS. 8000^5 (Bigger)
(Smaller) 40^10 VS. 8000^10 (Bigger)
Smaller x Smaller = Smaller

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5
Q

WEIGHTED AVERAGE
A school has 120 Juniors with an average final exam score of 90 and 100 Seniors with an average final exam score of 94.
A) The average of the Junior’s and Senior’s final exam scores combined.
B) 92

A

B) 92
Total of all scores 120 (90) + 100 (94)
Calculator: ———————- = —————————– = 91.818…
# of people 120 + 100
91.818…

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6
Q

BREAK THE CODE

x = -x

A

x = 0

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7
Q

BREAK THE CODE

x^2

A

0

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8
Q

BREAK THE CODE

x^3

A

x

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9
Q

BREAK THE CODE

x^3 > x^2

A

1

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10
Q

EXPONENTS

a^1/2 =

A

Square Root of “a”

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11
Q

EXPONENTS

a^-1/2

A

Square Root of “a”

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12
Q

INEQUALITIES

Recuerda que en inecualidades como esta: x^2 > 3x

A

Nunca hay que dividir entr una variable porque no sé su valor y por ende no sé si debo cambiar el signo.

x^2 > 3x

x^2/x > 3

x > 3

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13
Q

CAN YOU DISTRIBUTE?

(3x^2y)^2 =

A

Yes!
Dentro del paréntesis sólo hay multiplicaciones.
9 x^4 y^2

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14
Q

PERCENTS

37.5% =

A
  1. 375

* Es como dividir 37.5% entre 100 y al resultado quitarle el signo %

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15
Q

COMMON SENSE

What is the sum of the integers 1 to 11, inclusive, minus the average of those integers?

A

60
The average is the middle term, which is 6.
The sum of the integers 1 to 11, inclusive, is the average “times” the number of terms = 6*11 = 66
The answer is 66-6 = 60

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16
Q

DIGIT (also “Units Digit”)
¿De qué forma equivalente puedo plantear al 7 y al 5?
7 5
___ ___ ___ . ___ ___

A

7 5
___ ___ ___ . —- + —–
10 100
Porque 7 está en las Tenths y 5 en la posición de Hundreths.

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17
Q

EXPONENT
a^1/2 =

a^2/3 =

A

a^1/2 = Square Root of “a”

a^2/3 = Cubic Root of a^2

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18
Q

FRACTIONS
Which quantity is greater:
123/250 or 171/340

A

171/340

123/250 = La mitad de 250 es 125. 123 es menor que 125, entonces su valor (de la fracción inicial) es menor a 1/2.

171/340 = La mitad de 340 es 170. 171 es mayor que 170, por lo que su valor (de la fracción inicial) es mayor a 1/2.

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19
Q

FRACTIONS

Approximate (15/58) (9/19) 403

A

50
15/18 es más o menos 15/60, o más o menos 1/4.
9/19 es más o menos 9/18, o más o menos 1/2.
403 es apróximadamente 400.
La nueva multiplicación es: (1/4) (1/2) 400 = aproximadamente 50.
*El resultado exacto es 49.369, lo cual es muy cercano a 50.

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20
Q

PERCENT

What number is 150% greater than 60?

A 
150
60* + 90** = 150***
*60 es el valor original y siempre hay que sumarlo.
**El 150% de 60
***150 es 250% de 60
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21
Q

PERCENTS

70 is 250% greater than what number?

A

20
Utiliza fórmula:

x(1+250/100) = 70
x = 20
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22
Q

SIMPLE INTEREST

$5,000 invested for 6 months at an annual rate of 7% will earn how much?

A

175
Fórmula: Principal (P) x Rate (R) x Time (T) =
$5,000 (0.07) (0.5) = 175

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23
Q

DIGITS AND DECIMALS

Simplify (4 x 10^-2) - (2.5 x 10^-3)

A
  1. 0375

0. 0400 - 0.0025 = 0.0375

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24
Q

DIGITS AND DECIMALS

What is 4,563,021 / 10^5, rounded to the nearest whole number?

A

46
This yields 45.63021. To round to the nearest whole number, look at the tenths place. The digit in the Tenths place, 6, is more than 5. Therefore, is closes to 46.

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25
Q

FRACTIONS, DECIMALS AND PERCENTS

Strategy Tip: When fractions contain exponents and you have to plug in numbers for the exponents, always plug:

A

0 and , first.

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26
Q

SUMA DE ENTEROS CONSECUTIVOS

¿Cuál es la fórmula?

A 
 2
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27
Q

GRE CODE

¿Qué significa |z|

A

“z” es un número que, en la línea númerica, cae entre -1 y 1, inclusive.

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28
Q

GRE CODE
En problemas de “at the same time”, por ejemplo: “3 doctores agendan cada una de sus consultas en un horario específico distinto (cada determinados minutos, uno cada media hora, otro vada 50 munutos, etc), durante el día. ¿En qué hora del día cada uno de los doctores estaría teniendo su consulta al mismo tiempo (las 3 consultas ocurriendo simultáneamente)?

A

“at the same time do all three doctors schedule their appointments to begin at the same time?…”
Debo reconocer que se trata de un “Least Common Multiple” problem.
Una vez que obtenga este número puedo trabajar con él o con sus múltiplos.

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29
Q

GRE CODE

En problemas “What is the sum of the terms of the sequence from the 150th term to the 154th term”, necesitas reconocer:

A

La clave para resolver el problema es su posición, cuyo numero tiene múltiplos.
En la secuencia: 1, -3, 4, 1, -3, 4, 1, -3, 4… ¿Cuál es término 150th?

Reconce que el “4” está en la posición 3, y en la 6, 9, 12…
Entonces, el número 150th al ser también múltiplo de 3, también debe ser “4”.

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30
Q

GRE CODE

“If twice as many employees work at the Plant in Mexico as work at the Plant in Pakistan…”

A 
Mexico = 2P
Pakistan = P
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31
Q

ALGEBRA

¿De qué manera puedo simplificar la expresión: 2^-2y ?

A

4^-y
(2^2)^-y = 4^-y
Sólo llevé el 2 (sin el signo negativo), hacia dentro del paréntesis de la base 2. Por ello lo convertí en 4.

32
Q

COORDINATE PLANE
Cuando trabaje con una línea definida por una expresión algebráica:
4x + 3y = 60, un BUEN primer paso es:

A

Sustituir individualmente “x” y “y”, por cero, respectivamente.
En la ecuación 4x + 3y = 60, cuando “x” es cero, “y” es 20.
Cuando “y” es cero, “x” es 15.
Si hay que confirmar la posición de coordenadas dentro de un triángulo, piensa en una inecualidad, para probar cada una de las coordenadas. Ya sea 4x + 3y 60; me darán información para decidir cuál funciona, por ejemplo algún valor de “x” o de “y” que habría que sustituirse en 4x + 3y ? 60

33
Q

PERCENT

¿Cuál es el múltiplo para calcular un cambio de porcentaje del -8.8% de 102?

A

0.912

1 - 0.088 = 0.912
(102) (0.912) = 93.024

34
Q

PERCENT

The percent difference is equal to the actual difference divided by the basis of the comparison, which is:

A

It is what follows the word “than” in the problem statement.

35
Q

“A shipping company charges a shipping fee that varies depending upon the weight of the package to be shipped. The price to ship all packages weighing less than or equal to 5 pounds is $2.80, and an additional $0.25 is charged for each additional pound above 5 pounds. If the cost to ship Package A is greater than $7 but less than $8, which of the following could be the weight of Package A in pounds?”
A) 22 C) 24 E) 26
B) 23 D) 25

A 
A) 22  C) 24  
B) 23  D) 25
GRE CODE: Inequalities.
C = Cost
P = weight in pounds
Costo = $2.80 + $0.25 x (P - 5)
 Despeja "P" de la Inequality: 
$7
36
Q

FRACTIONS AND EXPONENTS

Recuerda que cualquier número elevado a la potencia -1, es igual a:

A

Su “reciprocal”.

37
Q

ROUNDUNG TO NEAREST DOLLAR

42,871.5

A

42872
Tengo que irme al número en la posición de las Tenths (primero a la derecha del punto decimal. Y “subo” o “bajo” el de las Unidades.

38
Q

POWERS OF 10

(0. 1)^2 =
(0. 1)^3 =

A

(0. 1)^2 = 0.01

(0. 1)^3 = 0.001

39
Q

DIGITS

What is the units digit of 2^50?

A

4
Units digit of 2 repeat in a cycle 2,4,8,6. Son 4 números.
Busco el número menor a 50, que sea divisible entre 4: 84. Tal marca el fin del ciclo.
Entonces, 2^48 = 6, 2^49 = 2, 2^50 = 4

40
Q

GRE CODE

Three pumps, P, R, and T, working simultaneously at their respective constant rates, can fill a tank in 5 hours.

A

1 1 1 1
—- + —- + —- = —-
P R T 5

41
Q

PERCENT

15.789% to the nearest 0.1 percent?

A

15.8%

42
Q

POWERS

(2x^-4) =

A

x^4

43
Q

NUMBER OF TERMS

Formula =

A

Last - First
————— +1
Spacing

44
Q

SQUARE ROOTS

Square Root of 25 x 10^8?

A

5 x 10^4

La potencia de “10^8” se fue a la mitad: “4”

45
Q

PERCENTS

66.666666666…%, to the nearest whole percent is?

A

67%

No 66%, porque el .6666666…% es mayor a .5 y por tanto, más cerca de 67%

46
Q

FRACTIONS TO DECIMAL
1
—- =
8

A

0.125

47
Q

FRACTIONS TO DECIMAL
3
—- =
8

A

0.375

48
Q

FRACTIONS TO DECIMAL
5
—- =
8

A

0.625

49
Q

FRACTIONS TO DECIMAL
7
—- =
8

A

0.875

50
Q

POWERS

(Square Root of 3)^4 =

A

9

The Radical cancel with a power of 2, an we are left with 3^2 = 9

51
Q

SCIENTIFIC NOTATION

5.5 billion =

75 million =

A

5.5 billion = 5, 500, 000, 000 = 5.5 x 10^9

75 million = 75, 000, 000 = 75 x 10^6

*Scientific Notation is the way to handle such large numbers on the GRE!!!!!!

52
Q

POSITIVE OR NEGATIVE

Watch out for the word “non-negative”, which means:

A

“Positive or zero”.

53
Q

ALGEBRA
Recuerda que para saber el valor mínimo de una función f(x), es muy probable que me den una ecuación cuadrática, por ejemplo:
f(x) = x^2 + 4x - 5
¿Cuál es el procedimiento para calcular el valor mínimo de dicha función?

A

-9

  1. Resolver la ecuación:
    (x-1) (x+5) =
    x= 1, -5
  2. Una Cuadrática alcanza su valor extremo a la mitad de las dos soluciones:
    1 + (-5)
    ———– = -2
    2
  3. Plug in de -2 en la función original:
    f(-2) = 4 + 4(-2) - 5 = -9
54
Q

INEQUALITIES

Si “y” es negativa, despeja 4x > y =

A

4x

—–

55
Q

INEQUALITIES

Despeja |-x| >_ 6

A

Tengo que considerar dos versiones:

“x” positiva: x >_ 6

“x” negativa: x

56
Q

INEQUALITIES
Despeja:

|x+4|
——– > 5
2

A

|x+4| > 10
Ahora, tengo que considerar dos posibilidades, que |x+4| sea positivo:
x+4 > 10 x > 6

Y que |x+4| sea negativo:
-x-4 > 10
-x > 14
x

57
Q

INEQUALITIES

Despeja a - b > a + b

A

a - b > a + b

  1. a - a - b > b
  2. -b > b
  3. 0 > 2b
  4. 0 > b = b es negativo.
58
Q

INEQUALITIES
¿Cómo cambio la dirección del signo?

b - c

A

Multiplico ambos lados de la Inequality por -1

-1 (b - c 0

59
Q

DECIMALS AND FRACTIONS
Quantitative Comparison

A) (0.25)^-3
B) 1/2^-6

A 
A) (0.25)^-3
0.25 es lo mismo que 1/4. Si tengo una cantidad elevada a una potencia negativa, es lo mismo que el reciprocal de dicha cantidad pero con la potencia positiva:
A)
1/1
-------- = 4^3 = (2^2)^3 = 2^6
1
---
4^3
B) 
1/1
--------- = 2^6 
1
---
2^6           Las dos cantidades son iguales = C
60
Q

GEOMETRY
Recuerda que un triángulo con dos lados iguales es un triángulo Isosceles, por lo que los ángulos opuestos a dichos lados iguales miden:

A

45 grados.
Si sé que uno de los lados mide 90 grados, en automático sé que el resto de los dos mide 45 grados cada uno.
Entonces, cualquier “Right Isosceles Triangle” es por definición un
45-45-90 Triangle.

61
Q

COORDINATE GEOMETRY

If line L has the equation 2x + 3y - 2 = 0, what is the slope of a line perpendicular to line L?

A

3/2
Reescribe la ecuación de L, en formato y-intercept =
y = -2/3x + 2/3
Entonces, la slope de la línea L es -2/3.
Siempre, la slope de una línea perpendicular es la “negative reciprocal” de la slope, en este caso: 3/2

62
Q

POWERS

5^5 + 5^5 + 5^5 + 5^5 + 5^5 =

A

5^6
Si pienso en 5^5 como si fuera “x”, podría reescribir la expresión original: x + x + x + x + x = 5x

Miremos la expresión original =
5^5 + 5^5 + 5^5 + 5^5 + 5^5 = 5(5^5)

Ahora, simplifiquemos:
5(5^5) = 5^1(5^5) = 5^1+5 = 5^6

La respuesta correcta es 5^6

63
Q

ROOTS AND POWERS
¿Qué puedo saber de las variables “x” y “y” a partir de la siguiente expresión?

(Square Root of x) - (Square Root of y) = 0

A

Square Root of x = Square Root of y

Entonces, x = y

64
Q

WORD PROBLEMS
Robert rode his moped for a total of 120 miles. He rode the first part of the trip at a constant speed of 20 miles per hour, and rode the remainder of the trip at a constant speed of 30 miles per hour.
1. What is Robert’s total time for the trip if he rode an equal time at each speed?
2. What is Robert’s total time for the trip if he rode an equal distance at each speed?

A
  1. 24/5
    D = RT
    Distance for first part of the trip = 20t
    Distance for second part of the trip = 30t
    20t + 30t = 120, or 50t = 120
    t = 12/5, entonces Total Time, t + t = 24/5
  2. Each portion of the trip = 60
    D = RT —> T (first part of the trip) = 60/20 = 3
    T (second part of the trip) = 60/30 = 2
    Total time = 3 + 2 = 5 hours
65
Q

WORD PROBLEMS / WEIGHTED AVERAGE
A convenience store currently stocks 48 bottles. The bottles have two sizes of either 20 or 40 ounces each. The average volume per bottle the store currently has in stock is 35 ounces. How many 40 ounce bottles are in stock?

A

36
Let x = the number of 20 oz. bottles.
48-x = the number of 40 oz. bottles.

The average volume of the 48 bottles in stock can be calculated as a weighted average:
x(20) + (48-x)(40)
----------------------- = 35
   48
x = 12
48-12 = 36
66
Q

WORD PROBLEMS
Jennifer has 60 dollars more than Brian. If she were to give Brian 1/5 of her money, Brian would have 25% less than the amount that Jennifer would then have. How much money does Jennifer have?

A 
$100
Jennifer money = J
Brian money = B
J = B + 60
She would have: j-(1/5)j = 4/5j
Brian would then have: b + (1/5)j dollars.

Since Brian’s amount of money would be 75% of Jennifer’s, we can create another equation: b + (1/5)j = (.75)(4/5)j

b + 1/5j = (.75) (4/5j)
b = 3/5j - 1/5j
b = 2/5j
Regresamos a la primera ecuación:
j = b + 60
j = 2/5j + 60
3/5j = 60
j = 100
67
Q

FRACTIONS
¿Cómo elimino el denominador “2” de las siguientes fracciones?

x+8 y+9
——– = ———
2 2

A

Multiplico ambos lados por “2”

2 (x+8) 2 (y+9)
———– = ———
2 2

Y los “2” se cancelan dejando:
x+8 = y+9

68
Q

FORMULA

Profit =

A

Profit = Revenue - Cost

69
Q

ALGEBRA

Expand x^4 - y^4

A
  1. x^4 - y^4
  2. (x^2)^2 - (y^2)^2
  3. (x^2 + y^2) (x^2 - y^2)
  4. (x^2 + y^2) (x + y) (x - y)
70
Q

GEOMETRY
Recuerda estar alerta para reconocer Triángulos 30-60-90, que pueden aparecer en Rectángulos.
¿Cuál es su proporción?
¿Cuáles son las 2 principales “pistas”?

A

Short Leg Long Leg Hypotenuse
x Square Root of 3 2x

  1. Triángulo Recto y uno de los lados es Square Root of 3 o múltiplo.
  2. La Hipotenusa es el doble de uno de los lados.
71
Q

SEQUENCES
Arithmetic Sequences* can be written in this form:

*Arithmetic Sequences: Ejemplo: “the term “n” is cefined by this formula..; what is the sum of the first 75 terms”.

A 
Termino "n" = a~Sub1 + k(n-1)
k = added constant.
n = number of the desired term.
Si "n" es 75 y "k" es 5 =   1+5(74)=371
Para calcular la suma de términos = 
(Average Value of Terms) (Number of Terms)

Average Value of Terms = Last + First
——————
2

72
Q

EXPONENTS

(1/2)^-2 * (1/3)^-3 * (1/4)^-4 =

A

2^2 * 3^3 * 4^4 = 6,912

Negative exponents lead to use the reciprocal of a number.

73
Q

INEQUALITIES
The equation:
|m+n| = |m| + |n|
can only be true if…

A

“m” and “n” have the same sign.

Either both have to be positive or negative.

+ + - -

74
Q

INEQUALITIES
¿Qué necesito para que la siguiente Inecualidad sea verdadera?

|p| - |q| = |p-q|

A

1) Que ambas variables tengan el mismo signo.
(+) (+) or (-) (-)

2) |p| >_ |q|

75
Q

STATISTICS
Otra forma para calcular el “Average” de un set de números igualmente espaciados, es:

“Quantity A: Average of the first 30 positive even numbers”.
“Quantity B: Average of the first 20 positive multiples of 3”.

A 
Quantity B is greater.
In Quantity A, the first number is 2 while the last number is 2 x 30 = 60.
Their Average equals:
2 + 60
--------- = 31
  2
In Quantity B, the first number is 3 and the last number is 3 x 20 = 60, such that the Average equals:
3 + 60
--------- = 31.5
  2

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