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#70 GMAT 2017

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by [email protected] » Thu Oct 27, 2016 12:02 pm
Hi jmacym,

This question can be solved by TESTing VALUES. I'm going to give you a couple of hints to get you started (so that you can finish the problem on your own):

1) To start, choose a small value for P (try P = 2).
2) Next, solve for R.
3) Plug P = 2 into the answer choices (make sure to check all 5). Which of them equals the value for R that you solved for?

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by GMATGuruNY » Thu Oct 27, 2016 12:03 pm
If p≠0 and p - (1-p²)/p = r/p, then r = ?

A. p + 1
B. 2p - 1
C. p² + 1
D. 2p² - 1
E. p² + p - 1
Plug in for p and solve for r.
Let p=2.
Substituting p=2 into p - (1-p²)/p = r/p, we get:
2 - (1-2²)/2 = r/2
2 - (-3/2) = r/2
7/2 = r/2
r = 7.

The target value is r=7.
Now plug p=2 into the answer choices to see which yields the target value of 7.
Only D works:
2p² - 1 = 2(2²) - 1 = 7.

The correct answer is D.
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by DavidG@VeritasPrep » Thu Oct 27, 2016 2:12 pm
Quote:
If p≠0 and p - (1-p²)/p = r/p, then r = ?

A. p + 1
B. 2p - 1
C. p² + 1
D. 2p² - 1
E. p² + p - 1
Or do a little algebra. Multiply both sides by 'p' to get p*p - (1-p²) = r
Simplify: p^2 - 1 + p^2 = r
And we get 2p^2 -1 = r; Answer is D
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by Matt@VeritasPrep » Thu Oct 27, 2016 11:08 pm
Multiplying both sides by p is probably the easiest first step:

p² - (1 - p²) = r

Then the negative sign is applied to both terms in the ( )'s, giving us:

p² - 1 -(-p²) = r

or

2p² - 1 = r
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