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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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Joined: 14 Mar 2010
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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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Updated on: 18 Sep 2018, 21:05
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Difficulty:

45% (medium)

Question Stats:

70% (01:47) correct 30% (01:47) wrong based on 345 sessions

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If $$P(r)=\frac{8r}{(1-r)}$$, for what value of r does $$P(r)=\frac{1}{2}P(3)$$?

A. 6
B. 3
C. 0
D. –3
E. –6

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Originally posted by monir6000 on 20 May 2012, 01:38.
Last edited by Bunuel on 18 Sep 2018, 21:05, edited 2 times in total.
Edited the question and added the OA
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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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20 May 2012, 04:21
8
1
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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##### General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 56244
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, 07:00
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 Sep 2018, 21:02
I have a question.
Isn't it kind of confusing,
P(r)=1/2(P(3)) could be
either
P(r)=1/(2(P(3)))
or
P(r)=(1/2)(P(3))
?
how do you guys know it is P(r)=(1/2)(P(3))?
VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
WE: Supply Chain Management (Energy and Utilities)
If P(r)=8r/(1-r), for what value of r does P(r)=1/2(P(3))?  [#permalink]

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18 Sep 2018, 21:13
Xica wrote:
I have a question.
Isn't it kind of confusing,
P(r)=1/2(P(3)) could be
either
P(r)=1/(2(P(3)))
or
P(r)=(1/2)(P(3))
?
how do you guys know it is P(r)=(1/2)(P(3))?

Hi Xica,
Notice that P(r)=$$\frac{1}{2}$$*P(3) is given in the question stem.

All other equations furnished are assumptions at your end.

You see that P(r)=$$\frac{1}{2P(3)}$$ is different from what has been given in question stem.

You may raise further queries (if any).
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If P(r)=8r/(1-r), for what value of r does P(r)=1/2(P(3))?   [#permalink] 18 Sep 2018, 21:13
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