If u(u+v) is not equal to 0 and u>0, is 1/u+v < 1/u + v ?
1) u+v>0
2) v>0
OAB
u(u+v) is not equal to 0 and u>0
This topic has expert replies
- 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
Statement 1: u+v > 0If u(u+v) ≠0 and u > 0, is 1/(u+v) < 1/u + v?
1) u+v >0
2) v>0
Plugging u=1 and v=1 into 1/(u+v) < 1/u + v, we get:
1/(1+1) < 1/1 + 1
1/2 < 2.
YES.
Plugging u=2 and v=-1 into 1/(u+v) < 1/u + v, we get:
1/(2-1) < 1/2 - 1
1 < -1/2.
NO.
Since in the first case the answer is YES, but in the second case the answer is NO, INSUFFICIENT.
Statement 2: v>0
Since all of the values are positive, we can rephrase the question stem.
Is 1/(u+v) < 1/u + v?
Put the right side over a common denominator:
1/(u+v) < (1+uv)/u
Cross-multiply:
u < (u+v)(1+uv)
Distribute on the right-hand side:
u < u + u²v + v + uv².
Subtract u from each side:
0 < u²v + v + uv².
Question stem, rephrased:
Is u²v + v + uv² > 0?
Since all of the values on the left-hand side are positive, the answer is YES.
SUFFICIENT.
The correct answer is B.
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