tricky 1 from Prep
This topic has expert replies
- [email protected]
- Master | Next Rank: 500 Posts
- Posts: 218
- Joined: Wed Dec 11, 2013 4:02 am
- Thanked: 3 times
- Followed by:4 members
GMAT/MBA Expert
- ceilidh.erickson
- GMAT Instructor
- Posts: 2095
- Joined: Tue Dec 04, 2012 3:22 pm
- Thanked: 1443 times
- Followed by:247 members
There isn't an obvious way to rephrase this question. We can't cross-multiply because we don't know whether p is negative. (You could rephrase giving yourself a positive and negative case, but this can become confusing). The best thing to do it to try to PROVE INSUFFICIENCY when looking at the statements.
Question: Is (1/p) > r/(r^2 + 2) ?
1) p = r
Test values to prove insufficiency:
If p and r both equal 1: (1/1) > 1/(1^2 + 2) --> 1 > 1/3 yes.
If p and r both equal -1: (1/-1) > -1/((-1)^2 + 2) --> -1 > -1/3 no.
Insufficient.
2) r > 0
This tells us nothing about p. Insufficient.
1 & 2) Together, if r > 0 then p > 0. We only need to test positive values:
If p and r both equal 1: (1/1) > 1/(1^2 + 2) --> 1 > 1/3 yes.
If p and r both equal 2: (1/2) > 2/(2^2 + 2) --> 1/2 > 2/6 yes.
If p and r both equal 3: (1/3) > 3/(3^2 + 2) --> 1/3 > 3/11 yes.
Any positive value we test would give us a "yes" result. The answer is C.
Question: Is (1/p) > r/(r^2 + 2) ?
1) p = r
Test values to prove insufficiency:
If p and r both equal 1: (1/1) > 1/(1^2 + 2) --> 1 > 1/3 yes.
If p and r both equal -1: (1/-1) > -1/((-1)^2 + 2) --> -1 > -1/3 no.
Insufficient.
2) r > 0
This tells us nothing about p. Insufficient.
1 & 2) Together, if r > 0 then p > 0. We only need to test positive values:
If p and r both equal 1: (1/1) > 1/(1^2 + 2) --> 1 > 1/3 yes.
If p and r both equal 2: (1/2) > 2/(2^2 + 2) --> 1/2 > 2/6 yes.
If p and r both equal 3: (1/3) > 3/(3^2 + 2) --> 1/3 > 3/11 yes.
Any positive value we test would give us a "yes" result. The answer is C.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Alternate approach:Is 1/p > r/(r^2 + 2) ?
(1) p = r
(2) r > 0
Statement 2 is clearly INSUFFICIENT.
Statement 1: p=r
Substituting p=r into the question stem, we get:
1/r > r/(r² + 2)?
(1/r) - r/(r² + 2) > 0?
(r² + 2 - r²) / [r(r² + 2)] > 0?
2 / [r(r² + 2)] > 0?
1 / [r(r² + 2)] > 0?
Case 1: r>0
1 / [r(r² + 2)] > 0
1/(positive*positive) > 0
1/positive > 0.
positive > 0.
In this case, the answer is YES.
Case 2: r<0
1 / [r(r² + 2)] > 0
1/(negative*positive) > 0
1/negative > 0
negative > 0.
In this case, the answer is NO.
INSUFFICIENT.
Statements combined:
Since only Case 1 is possible, the answer to the question stem is YES.
SUFFICIENT.
The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
- sanju09
- GMAT Instructor
- Posts: 3650
- Joined: Wed Jan 21, 2009 4:27 am
- Location: India
- Thanked: 267 times
- Followed by:80 members
- GMAT Score:760
(1) If p = r, let's plug in p = r = 2, and ask if ½ > 2/6, we get a YES. Or if we plug in p = r = -2, and ask if -½ > -2/6, and we get a NO. Hence, insufficient![email protected] wrote:
(2) It only tells about r, no info about p. Hence, insufficient!
When taken together, since both p and r are equal and positive, even if we now try a fraction for p and r, like if we plug in p = r = ½, and ask if 1/(½) > (½) /(¼ + 2) or "Is 2 > 2/9", we still get a YES. [spoiler]Hence Sufficient!
Take C[/spoiler]
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com