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If r = (3p + q)/2 and s = p q, for which of the following

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Manager
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If r = (3p + q)/2 and s = p q, for which of the following [#permalink] New post 24 May 2007, 14:01
If r = (3p + q)/2 and s = p – q, for which of the following values of p would r^2 = s^2 ?

a) 1/5q
b) 10 - (3/2q)
c) q - 1
d) 3q
e) (9/2q) - 9
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 [#permalink] New post 24 May 2007, 14:50
since r^2 = s^2 |r| = |s|

replace r with |p - q|

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

2p - 2q = 3p + q

p = -3q

Since its the absolute value of s the answer is:

d) 3q
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 [#permalink] New post 24 May 2007, 18:18
correct answer is actually A, not sure how to get it since there is no explanation.
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 [#permalink] New post 24 May 2007, 18:23
riverripper wrote:
since r^2 = s^2 |r| = |s|

replace r with |p - q|

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

2p - 2q = 3p + q

p = -3q

Since its the absolute value of s the answer is:

d) 3q


One problem I have with this:

If it is an absolute value then,

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

OR

|p - q| = -[(3p + q)/2] = (-3p - q)/2

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

2p - 2q = -3p - q
q = 5p

p = 1/5q


Guess I answered my own question :-D

I think D is put in as a trick answer.
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Re: From the web - need help [#permalink] New post 25 May 2007, 05:50
salr15 wrote:
If r = (3p + q)/2 and s = p – q, for which of the following values of p would r^2 = s^2 ?

a) 1/5q
b) 10 - (3/2q)
c) q - 1
d) 3q
e) (9/2q) - 9


Its A.

(There is a mistake in option A, option should be q/5 and not 1/5q)

Solve from the options.

Put the value of p = q/5 and solve for r and s; the value will be 4q/5

for both r and s.
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 [#permalink] New post 25 May 2007, 06:36
sorry that was a typo by me, should be (1/5)q and not 1/5q.
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Re: From the web - need help [#permalink] New post 25 May 2007, 07:26
salr15 wrote:
If r = (3p + q)/2 and s = p – q, for which of the following values of p would r^2 = s^2 ?

a) 1/5q
b) 10 - (3/2q)
c) q - 1
d) 3q
e) (9/2q) - 9


I got A.

Solve for p when r^2=s^2, which is same as [(3p+q)/2]^2 = (p-q)^2
--> (9p^2+6pq+q^2)/4 = p^2-2pq+q^2 *multiply 4 on both sides*
--> 9p^2+6pq+q^2 = 4p^2-8pq+4q^2 *simplify*
--> 5p^2+14pq-3q^2=0 *factor*
--> (5p-q)*(p+3q)=0 *solve*
--> p=q/5 OR p=-3q

Since -3q isn't in one of the answer choices, the answer must be A.
Re: From the web - need help   [#permalink] 25 May 2007, 07:26
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