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GRE Practice - Quantitative Reasoning - Set 14

  1. For which of the following expressions is it true that the value of the expression is the same for x = 37 as for x = -37? Select all that apply.
  1. |1 – x|2
  2. 1 – x2
  3. (1 – x)2
  4. x2 / ∣x∣2

Let’s consider each option.
A: don’t be fooled by the modulus(absolute value) sign. In this case, 1- x will be very different depending on x = -37 or 37.
B: x2 will be the same irrespective of x = -37 or 37 so 1- x2 will also be the same. SELECT
C: 1- x will be very different depending on x = -37 or 37, and so will (1 – x)2
D: x2 = |x|2 substitute any small values to check. SELECT

  1. The operation ⊕ is defined by the equation x⊕y = (x−y) / (3x−y) . What is the value of (-2⊕2) – (2⊕-2)?

-2⊕2 = (-2-2)/(-6 -2) = -4/-8 = 0.5
2⊕-2 = (2+2)/(6+2) = 4/8 = 0.5
Difference is 0

  1. If a sequence of 10 consecutive odd integers with increasing values has 9 as its 9th term, what is the sum of the terms of the sequence?

Solution: Don’t jump to arithmetic progression formulae
If the first number in the series was 1, then the series would have progressed as 1, 3, 5, 7, 9
9 would be the 5th term. But 9 is the 9th term so the series must have started with the previous 4 odd numbers
-7, -5, -3, -1, 1, 3, 5, 7, 9, 11
Upon addition the positive and negative terms cancel out and we are left with 9+ 11 = 20

  1. If p = r/2, q = 3r/4, s = pq/r2, and t = (p+q) / (1+s) what is t in terms of r
  1. 9r/10
  2. 10r/11
  3. 5r/2
  4. 10r/3
  5. 55r/32

s = (r/2 x 3r/4)/r2 = (3r2/8)/r2 = 3r2/8r2 = 3/8
p+q = r/2 + 3r/4 = 5r/4
t = (5r/4)/(1+3/8) = (5r/4)/(11/8) = 40r/44 = 10r/11

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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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