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karthikpandian19
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Inequality
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Source: Beat The GMAT — Data Sufficiency |
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aneesh.kg
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Good problem.
Statement(1):
(x - y)(x + y) > 1
Since the product of two quantities is positive, either both of them are positive
for e.g.
x - y = 2 and x + y = 4
OR
both of them are negative
for e.g.
x - y = -2 and x + y = -4
INSUFFICIENT
Statement(2):
x/y + 1 > 0
x/y > -1
For x/y > 0, x and y are both positive (x + y > 0) or both are negative (x + y < 0)
We don't need the test the x/y < 0 case because this statement is already
INSUFFICIENT
Let's combine.
For x/y + 1 > 0 in Statement (2),
for both x > 0 and y > 0, as well as x < 0 and y < 0, there are values (when |x| > |y|) for which Statement (1) holds true.
So, even after combining x + y > 0 or x + y < 0.
[spoiler](E)[/spoiler] is the answer.
Thanks Mitch, realised my mistake after seeing your response.
Statement(1):
(x - y)(x + y) > 1
Since the product of two quantities is positive, either both of them are positive
for e.g.
x - y = 2 and x + y = 4
OR
both of them are negative
for e.g.
x - y = -2 and x + y = -4
INSUFFICIENT
Statement(2):
x/y + 1 > 0
x/y > -1
For x/y > 0, x and y are both positive (x + y > 0) or both are negative (x + y < 0)
We don't need the test the x/y < 0 case because this statement is already
INSUFFICIENT
Let's combine.
For x/y + 1 > 0 in Statement (2),
for both x > 0 and y > 0, as well as x < 0 and y < 0, there are values (when |x| > |y|) for which Statement (1) holds true.
So, even after combining x + y > 0 or x + y < 0.
[spoiler](E)[/spoiler] is the answer.
Thanks Mitch, realised my mistake after seeing your response.
Last edited by aneesh.kg on Thu May 10, 2012 4:20 am, edited 1 time in total.
Aneesh Bangia
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GMATGuruNY
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If x=3 and y=1, both statements are satisfied.karthikpandian19 wrote:Is x + y > 0 ?
(I) x² - y² > 1
(II) x/y + 1 > 0
In this case, x+y>0.
If x=-3 and y=-1, both statements are satisfied.
In this case, x+y<0.
Thus, the two statements combined are INSUFFICIENT.
The correct answer is E.
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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
