If r = 3p+q/2 and s = p q, for which of the following : PS Archive
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If r = 3p+q/2 and s = p q, for which of the following

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If r = 3p+q/2 and s = p q, for which of the following [#permalink]

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07 Feb 2007, 13:33
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If r = 3p+q/2 and s = p â€“ q, for which of the following values of p would r^2 = s^2 ?
(A) 1/5q
(B) 10-3/5q
(C) q-1
(D) 3q
(E) 9/2q-9
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07 Feb 2007, 14:35
r^2 = s^2
<=> |r| = |s|
<=> |3p+q/2| = |p â€“ q|
implies that:
3p+q/2 = p â€“ q <=> 2p = -3/2*q <=> p = -3/4*q
or
3p+q/2 = -(p â€“ q) <=> 4p = q/2 <=> p = q/8

So.... none?
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07 Feb 2007, 15:02
Fig wrote:
r^2 = s^2
<=> |r| = |s|
<=> |3p+q/2| = |p â€“ q|
implies that:
3p+q/2 = p â€“ q <=> 2p = -3/2*q <=> p = -3/4*qor
3p+q/2 = -(p â€“ q) <=> 4p = q/2 <=> p = q/8

So.... none?

I also get the same values for p so the answer is none
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08 Feb 2007, 09:19
ggarr wrote:
If r = 3p+q/2 and s = p â€“ q, for which of the following values of p would r^2 = s^2 ?
(A) 1/5q
(B) 10-3/5q
(C) q-1
(D) 3q
(E) 9/2q-9

If the question was actually r = (3p + q)/2 and the rest is the same.

Case 1: (3p + q)/2 = p - q ==> p = -3q
Case 2: (3p + q)/2 = q - p ==> p = q/5

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08 Feb 2007, 11:02
devilmirror wrote:
ggarr wrote:
If r = 3p+q/2 and s = p â€“ q, for which of the following values of p would r^2 = s^2 ?
(A) 1/5q
(B) 10-3/5q
(C) q-1
(D) 3q
(E) 9/2q-9

If the question was actually r = (3p + q)/2 and the rest is the same.

Case 1: (3p + q)/2 = p - q ==> p = -3q
Case 2: (3p + q)/2 = q - p ==> p = q/5

Or A ... If we consider 1/5q = q/5
Re: PS II 020707   [#permalink] 08 Feb 2007, 11:02
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