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AbeNeedsAnswers: Master | Next Rank: 500 Posts; Posts: 394; Joined: Sun Jul 02, 2017 10:59 amFollowed by: 5 members; Thanked: 1 times

by AbeNeedsAnswers » Mon Jul 03, 2017 8:39 pm

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

A) p + 1

B) 2p - 1

C) p^2+ 1

D) 2p^2 - 1

E) p^2 + p - 1

D

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Source: Beat The GMAT — Problem Solving | Mon Jul 03, 2017 8:39 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Jul 03, 2017 9:18 pm

AbeNeedsAnswers wrote:If p â‰ 0 and p - (1-p^2)/p = r/p, then r =

A) p + 1

B) 2p - 1

C) p^2+ 1

D) 2p^2 - 1

E) p^2 + p - 1

Let p=-1.

Substituting p=-1 into p - (1-pÂ²)/p = r/p, we get:
-1 - [1 - (-1)Â²]/-1 = r/(-1)
-1 - 0 = -r
-1 = -r
r = 1.

Since the question stem asks for the value of r, our target value is r=1.
Now plug p=-1 into the answers to see which yields our target value of 1.
Only D works:
2pÂ² - 1 = 2(-1)Â² - 1 = 1.

The correct answer is D.

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Mon Jul 03, 2017 9:26 pm

AbeNeedsAnswers wrote:If p â‰ 0 and p - (1-p^2)/p = r/p, then r =

A) p + 1

B) 2p - 1

C) p^2+ 1

D) 2p^2 - 1

E) p^2 + p - 1

D

We have p - (1-p^2)/p = r/p

=> [p^2 -(1-p^2)]/p = r/p; taking LCM of LHS

Since p â‰ 0, we can cancel p from both the sides.

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

=> r = p^2 -1 + p^2

[spoiler]r = 2p^2 -1[/spoiler]

The correct answer: D

Hope this helps!

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » Tue Jul 04, 2017 8:12 am

p - (1 - pÂ²)/p = r/p

Start by multiplying both sides by p:
p[p - (1 - pÂ²)/p = r/p]
pÂ² - (1 - pÂ²) = r
pÂ² - 1 + pÂ² = r
2pÂ² - 1 = r

The answer is D.

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Wed Jul 05, 2017 1:01 am

p - (1 - pÂ²)/p = r/p

multiply both sides by p:

pÂ² - (1 - pÂ²) = r

do the subtraction on the left side:

2pÂ² - 1 = r

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8207; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed Jul 12, 2017 4:27 pm

AbeNeedsAnswers wrote:If p â‰ 0 and p - (1-p^2)/p = r/p, then r =

A) p + 1

B) 2p - 1

C) p^2+ 1

D) 2p^2 - 1

E) p^2 + p - 1

Let's simplify the given equation p - (1-p^2)/p = r/p by multiplying both sides by p:

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

p^2 - 1 + p^2 = r

2p^2 - 1 = r

Answer: D

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[email protected]

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sat Jun 09, 2018 5:57 pm

Hi All,

We're told that P â‰ 0 and P - (1 - P^2)/P = R/P. We're asked for the value of R. This question can be solved in a couple of different ways, including by TESTing VALUES.

IF....P=2, then we have....

2 - [(1 - 4)/2] = R/2
2 - ( -3/2) = R/2
4/2 - (-3/2) = R/2
7/2 = R/2
7 = R

So we're looking for an answer that equals 7 when P=2. There's only one answer that matches...

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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