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# If K = (r/3)/((p + 2)/(p^2 - 2p - r^2)), what is the value of K ?

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Joined: 02 Sep 2009
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If K = (r/3)/((p + 2)/(p^2 - 2p - r^2)), what is the value of K ?  [#permalink]

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05 Mar 2019, 05:09
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Difficulty:

35% (medium)

Question Stats:

76% (02:02) correct 24% (02:26) wrong based on 25 sessions

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If $$K = \frac{\frac{r}{3}}{\frac{p + 2}{p^2 - 2p - r^2}}$$, what is the value of K ?

(1) r = 2p

(2) p = 5, and 2r − 2p = 2p

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Re: If K = (r/3)/((p + 2)/(p^2 - 2p - r^2)), what is the value of K ?  [#permalink]

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05 Mar 2019, 10:16
the question can be re-written as.

K = $$\frac{r}{3}*\frac{(p^2 - 2p - r^2)}{(p + 2)}$$

From S1:

r = 2p
Then K = $$\frac{2p}{3}*\frac{(p^2 - 2p - 4p^2)}{(p + 2)}$$ = $$\frac{(-3p-2)82p^2}{3p+2}$$ = -2p^2.
Still Insufficient.

From S2:

r = 10
p = 5
We can easily find the value of K
Sufficient.

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Re: If K = (r/3)/((p + 2)/(p^2 - 2p - r^2)), what is the value of K ?  [#permalink]

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05 Mar 2019, 10:38
Bunuel wrote:
If $$K = \frac{\frac{r}{3}}{\frac{p + 2}{p^2 - 2p - r^2}}$$, what is the value of K ?

(1) r = 2p

(2) p = 5, and 2r − 2p = 2p

$$K = \frac{\frac{r}{3}}{\frac{p + 2}{p^2 - 2p - r^2}}$$,

k= r/3 * (p-r)^2 / p+2

#1
r=2p
not sufficient
#2
p=5 or say
r-p=p
r=2p
r=10 & p=5
substiute in
k= r/3 * (p-r)^2 / p+2
we get k= 250/21
sufficient
IMO b
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Re: If K = (r/3)/((p + 2)/(p^2 - 2p - r^2)), what is the value of K ?   [#permalink] 05 Mar 2019, 10:38
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