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GRE Practice - Quantitative Reasoning - Set 17

  1. Which of the following must be true?
    Select all that apply.
  1. If ab < ac then b < c .
  2. If a2b < a2c then b < c .
  3. If b2 < c2 then b < c .

We are looking for statements which are DEFINITELY TRUE.
A: If ab < ac then b < c – FALSE. If a is negative, then b > c
B: If a2b < a2c then b < c – TRUE a2 is positive so dividing both sides by a2 gives b <c
C: If b2 < c2 then b < c – FALSE for b = 2 and a = -3, b2 < c2 but b > c

  1. If x and y are two consecutive even integers and 2x + y = 2(x – y) , what is the value of x + y ?

Let y = x + 2
2x + x + 2 = 2(x – (x+2))
3x + 2 = -4
x = – 2
y = 0

  1. Which of the following integers do NOT have a divisor greater than 1 that is the square of an integer?
    Select all that apply.

We need to find how many of these numbers have a perfect square as a factor.
12 is divisible by 4
25 is divisible by 25
38 is divisible by 2, 19, and 38 NO SQUARES
32 is divisible by 4 as well as 16
42 is divisible by 2, 3, 6, 7, 14, 21, 42 NO SQUARES

  1. When the integer N is divided by 6, the remainder is 3. Which of the following is NOT a multiple of 6?
    Select all that apply.
  1. N – 3
  2. N + 3
  3. 2N
  4. 3N
  5. 3N + 18

N divided by 6, leaves a remainder = 3
So N is of the form 6a + 3
A: N – 3 = 6a DIVISIBLE
B: N + 3 = 6a + 6 DIVISIBLE
C: 2N = 12a + 6 DIVISIBLE
D: 3N = 18a + 9 NOT DIVISIBLE
E: 3N + 18 = 3(N + 6) and N + 6 is 6a + 9 so NOT DIVISIBLE

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Q. If the function f(x) is defined as f(x) = 3(x + 1) + 7, then f(a − 2) =

  1. 3a + 5
  2. 3a – 9
  3. 3a + 10
  4. 3a – 4
  5. 3a + 4
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