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r = ½ (3 p + q) and s = p – q

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by sanju09 » Thu Sep 16, 2010 11:29 pm
If r = ½ (3 p + q) and s = p – q, for which of the following values of p would r^2 = s^2?
(A) q/5
(B) 10 – 1½ q
(C) q – 1
(D) 3 q
(E) 4½ q – 9



[spoiler]Source: https://www.west.net/~stewart/gmat[/spoiler]
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by goyalsau » Thu Sep 16, 2010 11:44 pm
Is it A,
If its A then i would like to see the short cut because i did is really lengthy.
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by sanju09 » Fri Sep 17, 2010 12:08 am
goyalsau wrote:Is it A,
If its A then i would like to see the short cut because i did is really lengthy.
[spoiler]yes[/spoiler]


If r^2 = s^2, then:

[½ (3 p + q)] ^2 = [p – q] ^2

Work it out, segregate zero on one side of the equation, then factor the quadratic expression into two binomials. Find the two roots of p by setting each binomial equal to 0; [spoiler]q/5[/spoiler] will be one of the two.
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by klmehta03 » Sun Sep 19, 2010 4:48 pm
yup the ans is A..
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by kaushiksin » Mon Sep 20, 2010 3:28 am
r = ½ (3 p + q) and s = p - q

Lets start with choice A

P = q/5
r = 1/2 (3q/5+q) = 1/2 (8q/5) = 4q/5

s = q/5-q = -4q/5

r^2 = s^2
16q^2/25 = 16q^2/25

Hence, the answer is (A)
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