Solution
x^2 - y^2 = (x+y)*(x-y).
Obviously if x^2 - y^2 is positive, either both (x+y) and (x-y) are positive or both are negative.
Consider first (1) alone.
We know (x-y) is positive but we do not know anything about (x+y).
For example consider x= 2 and y= -3. So (x-y) = 2 + 3 = 5 (a positive number) and (x+y)= -1.
So x^2 - y^2 = (x+y)*(x-y) = -5 which is a negative number.
If x= 7 and y = 5, then (x-y) = 2 (a positive number)and (x+y) = 12.
Also x^2 - y^2 =(x+y)*(x-y) = 12 * 2 = 24 which is a positive number.
So nothing definite can be said.
Hence (1) is not enough.
Consider (2) alone.
We know (x+y) is positive, but we know nothing about (x-y).
For example let x = 8 and y = 5, then (x+y) = 13(a positive number) and (x-y) = 3.
So x^2 - y^2 = (x+y)(x-y) = 39 (a positive number).
If x = 5 and y = 8 then (x+y) = 13 a positive number and (x-y) = -3
So x^2 - y^2 = (x+y)(x-y) = -39 (a negative number).
Since nothing definite can be said (2) alone is not sufficient.
On combining we have that both (x+y) and (x-y) are positive and so their product (x^2 - y^2) will also be positive.
So the answer to the question is yes.
The correct answer is (C).
Is x^2 – y^2 a positive number?
This topic has expert replies
Source: Beat The GMAT — Data Sufficiency |
GMAT/MBA Expert
-
Rahul@gurome
- GMAT Instructor
- Posts: 1179
- Joined: Sun Apr 11, 2010 9:07 pm
- Location: Milpitas, CA
- Thanked: 447 times
- Followed by:88 members
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
-
ayankm
- Senior | Next Rank: 100 Posts
- Posts: 48
- Joined: Mon Apr 19, 2010 3:08 pm
- Location: Brazil
- Thanked: 5 times
- Followed by:1 members
- GMAT Score:660
Thanks a lot Rahul.Rahul@gurome wrote: If x = 5 and y = 8 then (x+y) = 13 a positive number and (x-y) = -3
So x^2 - y^2 = (x+y)(x-y) = -39 (a negative number).
Since nothing definite can be said (2) alone is not sufficient.
On combining we have that both (x+y) and (x-y) are positive and so their product (x^2 - y^2) will also be positive.
So the answer to the question is yes.
The correct answer is (C).
Somehow I missed the situation where y>x and x-y would end up being negative.
