Quant Revisit List

Question 1

sqrt(3)

Answer 1

1.7

Question 2

sqrt(2)

Answer 2

1.4

Question 3

Put this into an equation:

Answer 3

Question 4

Draw 2 variable + total matrix for this problem:

Answer 4

Question 5

What are the steps to solve:

Answer 5

EASY

Process: 1) split 10 into factors (5*2)^n => (5^n * 2^n) so we have common base 2) solve for n

Question 6

What’s the median and mean for consecutive integers?

Answer 6

2,4,6,8 = MEDIAN=5, MEAN=5; for 1,2,3,4,5,6,7 then MEDIAN=4 and MEAN=4. Middle number is both mean and median.

Question 7

Answer 7

U got this bro!

Question 8

Count number of multiples of 3

Answer 8

(Last - First)/(multiple) + 1

Question 9

How many different ways can you draw an isocolies triangle 40 degree angle?

Answer 9

40,40,100; 40,70,70; etc.

Question 10

Imagine you’re given a triangle inside a square, if that triangle’s base is the diameter of the circle, and the triangle touches the outside of a circle. What do you know about this triangle?

Answer 10

I know that the triangle has a 90 degree angle at the point that touches the circle.

Question 11

(x+y)^2

Answer 11

x^2 + 2xy + y^2

Question 12

(x-y)^2

Answer 12

x^2 -2xy + y^2

Question 13

How to solve?

Answer 13

SUBTRACT AREAS! will need to create equation using each triangle

Question 14

((x^5)^4) =

Answer 14

x^20

Question 15

y^4 * y^9 =

Answer 15

y^13

Question 16

Sqrt(p*q) =

Answer 16

Sqrt(p)*Sqrt(q)

Question 17

Even * Odd * Even = ?

Answer 17

Even

Question 18

Odd * Even * Odd = ?

Answer 18

Even

Question 19

Factor 147

Answer 19

Methodology: go from smallest to biggest when prime factoring. Clearly not divisible by 2, because 147 is odd.

Next, check for divisibility by 3 – 1+4+7 = 12, so it’s divisible by 3. (or, better, notice that it’s 3 less than the round number 150, which is 3x50, so 147 is 3x49)

Question 20

How do we tell if something is divisible by 3?

Answer 20

If each digit summed up sums to something that is divisible by three, then the answer is YES.

Example: 147 divisible by 3? Is 3 a factor of 147? 1+4+7 = 12, therefore YES.

Question 21

Is 0 an integer?
Is 0 even?

Answer 21

YES

and

YES

Zero is both EVEN and an integer.

Question 22

Is 1 a prime number?

Answer 22

NO!

Question 23

Are any prime numbers even?

Answer 23

YES! 2 is the ONLY even prime number.

Question 24

What are the factors of 6?

Answer 24

1,2,3,6

Question 25

What are the multiples of 6?

Answer 25

6,12,18,24…

Question 26

How do we tell if a fraction will be finite or repeating?

Answer 26

If denominator as 2 and 5 as prime factors => NOT REPEATING

What is a prime factor?

The prime factors of 15 are 3 and 5 (because 3×5=15, and 3 and 5 are prime numbers).

Question 27

When X and Y are both positive integers and the remainder is 2:

Answer 27

x/y = integer + remainder / y

This can help solve modulo or remainder questions.

Question 28

if 0 < x < 1 then rank:

sqrt(x), x^2, and x from least to greatest order

Answer 28

x^2 < x < sqrt(x)

Question 29

x^2 * y^2 - 16 = ?

Answer 29

(xy - 4)(xy + 4)

Question 30

x^2 - 9 = ?

Answer 30

(x-3)(x+3)

Question 31

5/4 = 1 + 1/4

Answer 31

1 is the REMAINDER, the MODULO. Use example to memorize this equation from my intuition.

Question 32

|2x + 4| = 12, x=?

Answer 32

Solution: Solve the equation TWICE. once for when absolute value is positive, a second time for when it is negative:

POSITIVE:

2x + 4 = 12 therefore x = 4

NEGATIVE

-(2x+4) = 12 therefore x = -8

Question 33

sqrt(10,000) = ?

Answer 33

100

Question 34

If two absolute values are equal, what must be true of the expressions?

Answer 34

It must be true that the expressions with the absolute value bars are either equals or opposites.

So:

|expression1 | = |expression2|

becomes in the equals case:

( expression1 ) = ( expression2)

and in the opposite case:

( expression1 ) = -( expression2)

Similar to solving an absolute value, you must solve twice for the unknown

Question 35

Equation for compound interest:

Answer 35

A = P(1 + r/n)^nt

Question 36

Answer 36

Remember 5^(x-3) = 5^x / 5^3

Question 37

Answer 37

Question 38

Answer 38

this one will be hard to solve w/o paper due to math. But main point is to translate from question to equation DIRECTLY:

A = 0.36*C

Question 39

Answer 39

Note: translate equations directly from the question.

“mixture weights more than 20 ounces” => m > 20

Question 40

Answer 40

Property of parallelogram: opposite triangles are the same area. This helps us solve for the isosceles triangle.

Question 41

Answer 41

Note: it is important to rephrase (a) the information that is given, and (b) the question:

Question 42

Answer 42

Any scalar => can solve.

Question 43

Answer 43

GMAT Hack: turn the two digits into variables. Tens digit = 10*A, one’s digit = 1*B.

Note: Translate equations from text!

Question 44

If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be

(A) 2
(B) 5
(C) 6
(D) 7
(E) 14

Answer 44

Question 45

True of False: In a perfect square, the prime factors come in pairs

Answer 45

TRUE.

Question 46

How to tell if divisible by 11?

ex: is 143 divisible by 11?

Answer 46

Units digit and Hundreds digit sum to middle digit:

ex: is 143 divisible by 11?

1+3 = 4, therefore divisible by 11 !

Question 47

If n=12, how many positive and even divisors does n have, including n?

Answer 47

divisors of 12 = {1,2,3,4,6,12}

even divisors of 12 = {2,4,6,12}

therefore, 4.

Question 48

Answer 48

Question 49

Answer 49

the diagram is wrong. answer should read:

2^2 + 2(2) + 1 = (2+1)(2+1) = 3*3* = 9

Question 50

How do we know the area of an obtuse triangle?

Answer 50

still (1/2)*b*h, however the height is from the triangle that forms a right angle (see photo–blue triangle)

Question 52

If a given triangle has two sides taht are the same length, is it isocolies?

Answer 52

YES. and the two opposite angles are both the SAME angle as well.

This problem, for example, can’t be solved without knowing this:

Question 53

How many 2 person teams can be formed with persons 1,2,3,4,5,6,7, and 8?

Answer 53

8 choose 2 =

n! / ((n-k)! k!)

8! / ((8-2)! * 2! )

8*7 / 2

56 /2

28.

NOTE: team “1,2,3” is same as “3,1,2” and “2,1,3” therefore order doesn’t matter. This is why we use COMBINATIONS equation.