If u(u+v)neq{0} and u >0, is 1/(u+v) < 1/u + v?
(1) u+v >0
(2) v>0
I answered the above equestion as follow please correct me if I am wrong
1/(u+v)<1/u+v
1/(u+v) -1/u -v <0
1/(u+v) - (1-uv/u) <0
u-(u+v) - uv( u+v)/(u+v)u<0
u-u-uv-uv/u<0
-2uv/u <0
-2v<0 or does v positive?
can I devided both sides by -2 and it will be does v>o ?
If u(u+v)neq{0} and u >0, is 1/(u+v) < 1/u + v?
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.
Two take-aways:
1. When we're plugging values into a Yes/No DS question, we need to determine what types of values could change the answer from YES to NO or vice versa. Since statement 2 requires that v>0, the sign of v seems to be an issue here. Thus, we should consider NEGATIVE values when we plug into statement 1.
2. When an inequality problem is restricted to positive values, algebra becomes much easier to implement, since we don't have to worry about the direction of the inequality.
The steps in red contain algebraic errors and yield an incorrect rephrase of the question stem.Asma77 wrote:
I answered the above equestion as follow please correct me if I am wrong
1/(u+v)<1/u+v
1/(u+v) -1/u -v <0
1/(u+v) - (1-uv/u) <0
u-(u+v) - uv( u+v)/(u+v)u<0
u-u-uv-uv/u<0
-2uv/u <0
-2v<0 or does v positive?
can I devided both sides by -2 and it will be does v>o ?
I suggest that you check your work.
Last edited by GMATGuruNY on Sun Sep 18, 2016 3:03 am, edited 2 times in total.
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
OK, I see my mistake here so it will be u-(u+v)+uv(u+v)/u(u+v)<oGMATGuruNY wrote:Statement 1: u+v > 0massi2884 wrote:If 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, and in the second case the answer is NO, INSUFFICIENT.
Statement 2: v>0
Since all of the values are positive, we can rephrase the questions 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.
Two take-aways:
1. When we're plugging values into a Yes/No DS question, we need to determine what types of values could change the answer from YES to NO or vice versa. Since statement 2 requires that v>0, the sign of v seems to be an issue here. Thus, we should consider NEGATIVE values when we plug into statement 1.
2. When an inequality problem is restricted to positive values, algebra becomes much easier to implement, since we don't have to worry about the direction of the inequality.
The steps in red contain algebraic errors and yield an incorrect rephrase of the question stem.Asma77 wrote:
I answered the above equestion as follow please correct me if I am wrong
1/(u+v)<1/u+v
1/(u+v) -1/u -v <0
1/(u+v) - (1-uv/u) <0
u-(u+v) - uv( u+v)/(u+v)u<0
u-u-uv-uv/u<0
-2uv/u <0
-2v<0 or does v positive?
can I devided both sides by -2 and it will be does v>o ?
I suggest that you check your work.
u-u-v+uv(u+v)/u(u+v)<0
-v+uv/u<0
v(-1+u)/u<0
is that correct
- 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
Unfortunately, there are still algebraic errors.Asma77 wrote:
OK, I see my mistake here so it will be u-(u+v)+uv(u+v)/u(u+v)<o
u-u-v+uv(u+v)/u(u+v)<0
-v+uv/u<0
v(-1+u)/u<0
is that correct
When the lefthand side is put over a common denominator, you are neglecting to enclose the ENTIRE NUMERATOR in brackets.
As a result, the steps that follow are incorrect.
Putting all three terms over a common denominator seems quite messy, making the problem harder rather than easier.
I recommend that you opt for an alternate approach.
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