If P(r)=8r/(1-r), for what value of r does P(r)=1/2(P(3))? : GMAT Problem Solving (PS)
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# If P(r)=8r/(1-r), for what value of r does P(r)=1/2(P(3))?

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If P(r)=8r/(1-r), for what value of r does P(r)=1/2(P(3))? [#permalink]

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20 May 2012, 00:38
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If P(r)=8r/(1-r), for what value of r does P(r)=1/2(P(3))?

A. 6
B. 3
C. 0
D. –3
E. –6
[Reveal] Spoiler: OA

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Last edited by Bunuel on 20 May 2012, 11:32, edited 1 time in total.
Edited the question and added the OA
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20 May 2012, 03:21
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monir6000 wrote:
If P(r)=8r/(1-r), for what value of r does P(r)=1/2*(P(3))?

A. 6
B. 3
C. 0
D. –3
E. –6

P(r) = 8r / (1-r)

P(3) = 8*3 / ( 1-3 ) = - 12

1/2 * P(3) = - 6

P(r) = - 6

=> 8r / ( 1-r ) = - 6

=> 8r = 6r - 6

=> 2r = - 6

=> r = - 3
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If you found my contribution helpful, please click the +1 Kudos button on the left, Thanks

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20 May 2012, 03:28
thanks a lot.....very helpful +1 kudos...
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Re: If P(r)=8r/(1-r), for what value of r does P(r)=1/2(P(3))? [#permalink]

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17 Oct 2014, 02:18
If P(r)=8r/(1-r), for what value of r does P(r)=1/2(P(3))?

A. 6
B. 3
C. 0
D. –3
E. –6

Can someone explain this problem again? I got it till -12, but wasn't sure what to do after this? Thanks in advance!
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Re: If P(r)=8r/(1-r), for what value of r does P(r)=1/2(P(3))? [#permalink]

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17 Oct 2014, 06:00
Rca wrote:
If P(r)=8r/(1-r), for what value of r does P(r)=1/2(P(3))?

A. 6
B. 3
C. 0
D. –3
E. –6

Can someone explain this problem again? I got it till -12, but wasn't sure what to do after this? Thanks in advance!

$$P(r) = \frac{8r}{1-r}$$, so $$P(3) = \frac{8*3}{1-3} = - 12$$.

We need to find for what value of r does $$P(r)=\frac{1}{2}*P(3)$$, so for what value of r does $$P(r)=\frac{1}{2}*(-12)$$. So, we soulh solve for r the following: $$\frac{8r}{1-r}=\frac{1}{2}*(-12)$$ --> $$r=-3$$.

Check questions about functions in Special Questions Directory:

Operations/functions defining algebraic/arithmetic expressions
Symbols Representing Arithmetic Operation
Rounding Functions
Various Functions

Hope this helps.
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Re: If P(r)=8r/(1-r), for what value of r does P(r)=1/2(P(3))? [#permalink]

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18 Oct 2014, 03:18
Got it! Thank you so much Bunuel. I keep missing out on small stuff.
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Re: If P(r)=8r/(1-r), for what value of r does P(r)=1/2(P(3))? [#permalink]

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16 Jan 2016, 06:37
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