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
A. 1q/5
B. 10 - 3q/2
C. q - 1
D. 3q
E. 9q/2 - 9
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
