GRE Math Practice: Quantitative Problem Solving Practice Questions

GRE Math Practice: Quantitative Problem Solving

Numbers
All numbers are real numbers.
Figures

The position of points, lines, angles, etcetera, may be assumed to be in the order shown. All lengths and angle measures may be assumed to be positive. Lines shown as straight may be assumed to be straight. Figures lie in the plane of the paper unless otherwise stated. Figures that accompany questions are intended to provide useful information. However, unless a note states that a figure has been drawn to scale, you should solve the problems by using your knowledge of mathematics, and not by estimation or measurement.

Question 1

If the integer a is a multiple of 6, the integer b is a multiple of 3, and a>b>0, then
which of the following integers must be a2 – b2 multiple of?
A. 6
B. 8
C. 9
D. 10
E. 12

> Question 2

If a sweater sells for $48 after a 25 percent markdown, what was its original price?
A. $56
B. $60
C. $64
D. $68
E. $72

> Question 3

If x + y =8 and y- x = -2, then y=
A. -2
B. 3
C. 5
D. 8
E. 10

> Question 4

If r ♥ s= r(r-s) for all integers r and s, then 4♥(3♥5) equals
A. -8
B. -2
C. 2
D. 20
E. 40

> Question 5

If there are 14 women and 10 men employed in a certain office, what is the probability that one employee picked at random will be a woman?
A. 1/6
B. 1/14
C. 7/12
D. 1
E. 7/5

Answers and Explanations

1.C
We can use the strategy of Picking Numbers to solve this question. With the method  of Picking Numbers, all 4 incorrect answer choices must be eliminated because sometimes one or more incorrect answer choices will work for the particular values that we select. Let's let a = 6 and b = 3. Then a2 – b2 = 62 – 32 = 36 – 9 = 27. Looking at the answer choices, 27 is not a multiple of 6, 8, 10, or 12, which are the numbers in answer choices (A), (B), (D), and (E), respectively. So choices (A), (B), (D), and (E) can be eliminated. Now that all 4 incorrect answer choices have been eliminated, we know that choice (C) must be correct. Just to check, we see that 27 is a multiple of 9, which is to be expected since we have concluded that choice (C) must be correct.

2.C
We want to solve for the original price, the Whole. The percent markdown is 25%, so $48 is 75% of the whole: Percent x Whole = Part.
75% x Original Price = $48
Original Price = $48/0.75 = $64


3.B
When you add the two equations, the xs cancel out and you find that 2y= 6, so y=3.

4.E
Start in the parenthesis and work out: (3♥5)= 3(3-5)= 3(-2)= -6; 4♥(-6)=4[4-(-
6)]= 4(10)= 40

5.B
Probability = (Number of Desired Outcomes/Number of Possible Outcomes) =
(Number of Women/Number of People) = 14/24= 7/12.