If p 0 and p (1 p^2 )/p = r/p, then r =

Question

If p ≠ 0 and  p – \frac{(1 – p^2 )}{p} =\frac{r}{p} , then r =

A.  p + 1

B.  2p – 1

C.  p^2+ 1

D.  2p^2 – 1

E.  p^2 + p – 1

OG 2017 New Question

chetan2u · Accepted Answer

p –\frac{(1 – p^2 )}{p} = \frac{p^2 –(1 – p^2 )}{p} = \frac{p^2 –1 + p^2}{p} = \frac{2p^2 –1}{p} = \frac{r}{p} .................
 r= 2p^2-1

D

JeffTargetTestPrep · Answer

We are given that p -   = r/p, and we must isolate r.

We can start by multiplying the entire equation by p and then simplifying:

p^2 - (1 - p^2) = r

p^2 - 1 + p^2 = r

2p^2 - 1 = r

Answer: D

diegocml · Answer

p-\cfrac { \left( 1-{ p }^{ 2 } ight) }{ p } =\cfrac { r }{ p } \ \left  \ { p }^{ 2 }-\left( 1-{ p }^{ 2 } ight) =r\ { p }^{ 2 }-1+{ p }^{ 2 }=r\ 2{ p }^{ 2 }-1=r

PEMDAS in the 3rd line got me thinking whether I should multiply that negative to  \left( 1-{ p }^{ 2 } ight) .

Valentina86 · Answer

Bunuel. Once we multiply both sides by p, p in the numerator becomes p^2, but what happens to the p in the denumerator? I understand that it gets cancel, but I don't see how.

Bunuel · Answer

p – \frac{(1 – p^2 )}{p} =\frac{r}{p} ;

Multiply by p:  p*(p – \frac{(1 – p^2 )}{p}) =p*\frac{r}{p} ;

Expand the left hand side and reduce by p in the right hand side:  p^2 – p*\frac{(1 – p^2 )}{p} =r ;

Reduce by p in the second term on the left hand side:  p^2 –(1 – p^2 ) =r ;

Open the brackets:  p^2 –1 + p^2 =r ;

2p^2-1=r

Answer: D.

Hope it's clear.

avigutman · Answer

Video solution from Quant Reasoning:
 https://www.youtube.com/watch?v=xLXgzddHwNk

GMATinsight · Answer

Answer: Option D

Video solution by  GMATinsight

https://www.youtube.com/watch?v=RfJ8izUaGxQ

Kinshook · Answer

Asked: If p ≠ 0 and  p – \frac{(1 – p^2 )}{p} =\frac{r}{p} , then r =

p – \frac{(1 – p^2 )}{p} =\frac{r}{p} 
 \frac{(p^2 - 1 + p^2 )}{p} =\frac{r}{p} 
 \frac{(2p^2 - 1)}{p} =\frac{r}{p} 
r = 2p^2 - 1

IMO D

woohoo921 · Answer

avigutman 
Thank you! Would choosing a number for P to solve for R, and then testing the answer choices always work as well? Is this a good strategy? For instance, I said let P=2 and then R equaled 7 after I solved for R in the original. I then plugged in P=2 in the answer choices and only D yielded 7 for R.

avigutman · Answer

woohoo921  thanks for your question. That's a fine strategy for test day, but you should strive to get more out of a question when practicing at home, or else you miss an opportunity to "grow" as a test taker. See here for more:

https://www.youtube.com/watch?v=axcTDf-XidU

saynchalk · Answer

https://gmatclub.com/forum/download/file.php?id=84570 Would the answer be different if it was without the bracket? Bunuel chetan2u GMAT-Club-Forum-givgzqt1.png

Bunuel · Answer

No. Those two are the same:

p – \frac{(1 – p^2)}{p} = \frac{r}{p}

p – \frac{1 – p^2}{p} = \frac{r}{p} .

chetan2u · Answer

The negative sign is for entire fraction and fraction is read as one element.

p – \frac{(1 – p^2)}{p} = p – \frac{1 – p^2}{p} = p –( \frac{1 – p^2}{p}) .

If p 0 and p (1 p^2 )/p = r/p, then r =

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GMAT Problem Solving (PS) Questions

If p 0 and p (1 p^2 )/p = r/p, then r =

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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