If 2p/(p^2 - 2p + 1) = 1/4, then the value of p + 1/p is

Question

A) 8
B) 10
C) 12
D) 2√6
E) None of these

Bunuel · Answer

The question asks:  
 p+\frac{1}{p}=\frac{p^2+1}{p}=?

Given: 
 \frac{2p}{(p^2-2p+1)} = \frac{1}{4}

4*2p = p^2-2p+1

p^2 + 1 = 10p

Thus: 
 p+\frac{1}{p}=\frac{p^2+1}{p}=\frac{10p}{p}=10 .

Answer: B.

Hope it helps.

pushpitkc · Answer

Given  \frac{2p}{(p^2-2p+1)} = \frac{1}{4}  Now,  (p^2-2p+1) = 8p  --> 1

Now, since we are asked to find out the value of  p+\frac{1}{p} 
  p+\frac{1}{p}  =  \frac{p^2 + 1}{p}

\frac{p^2 + 1}{p}  =  \frac{p^2 + 1+ 2p - 2p}{p}  (Adding & subtracting 2p to the numerator of the expression)
=  \frac{p^2 + 1 - 2p}{p} + \frac{2p}{p}  
Substituting the value of  p^2 + 1 - 2p  from 1,
=  \frac{8p}{p} + 2  = 10(Option B)

TimeTraveller · Answer

p + 1/p = p^2 + 1/p

8p = p^2 - 2p + 1
p^2 - 2p + 1 - 8p = 0
p^2 - 10p + 1 = 0

p^2+1 = 10p

p^2+1/p = 10p/p = 10. Ans - B.

rulingbear · Answer

Interesting question, easy but could be missed if overthought. I think the trick is not to solve for p first but try to isolate the whole p+1/p. Cross multiplication gives p^2 - 10p + 1 = 0 ; p^2 + 1 = 10p ; p+1/p=10

In summary, collect like times and try to get rid of the exponent on p. Also,  a familiarity with the form p+1/p as quadratic will help see the connection.

giannilorenz · Answer

We are not informed that p is a nonzero number, right? So how can we divide the equation by p?

Bunuel · Answer

p cannot be 0 because p =0 does not satisfy 2p/(p^2-2p+1) = 1/4.

gvij2017 · Answer

I don't understand whether it is my mistake or author's mistake to read it (p+1)/p which is actually asked. 
Without that bracket, I think people like me could understand it p+ (1/p).

I am sure actual GMAT won't make such ambiguous question. 
Thanks!

Bunuel · Answer

The question ask to find the value of  p + \frac{1}{p} , not  \frac{p+1}{p} . Also, p + 1/p can only mean  p + \frac{1}{p} . If it were  \frac{p+1}{p} , it would have been written as (p+1)/p.

bumpbot · Answer

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If 2p/(p^2 - 2p + 1) = 1/4, then the value of p + 1/p is

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If 2p/(p^2 - 2p + 1) = 1/4, then the value of p + 1/p is

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