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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?
1. 20
2. 22
3. 28
4. 32
5. 40

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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