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by MBA.Aspirant » Tue Nov 15, 2011 3:02 pm
If r = (3p + q)/2 and s = p - q, for which of the following values of p would r^2 = s^2?

A. 1q/5
B. 10 - 3q/2
C. q - 1
D. 3q
E. 9q/2 - 9
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by shankar.ashwin » Tue Nov 15, 2011 4:27 pm
r^2 = s^2 -> r = +s

r = s (or) r = -s

Case 1: r =s

(3p + q)/2 = p-q
(3p+q) = 2(p-q)

3p + q = 2p - 2q

p = -3q (Not there in options, so do the other case)

Case 2: r = -s

(3p + q)/2 = -p+q

3p + q = -2p+2q

5p = q

p = q/5 A IMO
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by GmatMathPro » Tue Nov 15, 2011 4:28 pm
r^2=s^2 whenever r=s or r=-s

r=-s is the one that most people would overlook, so let's start with that one:

r=-s

(3p+q)/2=-(p-q)

(3p+q)/2=q-p

3p+q=2q-2p

5p=q

p=q/5

Ans: A
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