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GRE Practice - Quantitative Reasoning - Set 18

  1. If the product of even integer A and odd integer B is 630, where A≠2, B≠1 and A, B > 0, then which of the following must be true?
    Select all that apply.
  1. The largest value of A is 210
  2. B is a multiple of 3
  3. The smallest difference between A and B is 9

630 = 2 x 3 x 3 x 5 x 7
We are looking for statements which are DEFINITELY TRUE.
A: B≠1 and is odd so B can be 3 and A = 210
B: One of A and B must be multiple of 3 but it can be A alone A = 18, B = 35
C: A = 30 and B = 21 the smallest difference is 9

  1. If a + b – ab = 0 , which of the following CANNOT be a value of b ?

a + b – ab = 0
a(1-b) + b = 0
a = b / b−1
for b = 1 a is undefined so b cannot be 1

  1. When the integer N is divided by 12, the remainder is 3. Which of the following, when divided by 12, will have a remainder of 6?
    Select all that apply.

Answer: A, B, C

N divided by 12 leaves remainder of 3
So N is of the form 12k + 3
A: 2N = 24k + 6 remainder: 6
B: 6N = 72k + 18 remainder: 6
C: 4N + 6 = 48k + 12 + 6 = 48k + 18 remainder: 6

  1. What is the smallest positive integer n for which 400 is a factor of 10n ?

400 = 16 x 25 = 24 x 52
10n = 2n x 5n
Since we need at least 4 for the power of 2 so n = 4

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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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