Is x = y?

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crackthetest: Senior | Next Rank: 100 Posts; Posts: 40; Joined: Mon Feb 16, 2009 8:50 pm; Thanked: 3 times

by crackthetest » Mon Feb 16, 2009 9:02 pm

1) x^2 = y^ 2

2) x is +ve

OA is E

Statement 1 says x^2 = y^2, so if x is +ve then by equality y should also be +ve, else if x is -ve, y should also be.

shouldn't the answer be A? Please advise.

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Source: Beat The GMAT — Data Sufficiency | Mon Feb 16, 2009 9:02 pm

mdavis: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Thu Nov 20, 2008 2:18 pm; Thanked: 1 times

by mdavis » Mon Feb 16, 2009 9:16 pm

I think in one, you could have the situation where x is negative and y is positive, which means that both equal the same number when squared, but both could be a different number. For example, x=-3 and y=3. Both will equal 9 when squared but do not equal by themselves.

In two, there is nothing that tells us about the value of y. X can be any positive value, but we know nothing about y at all.

If you combine both 1 and 2 together, we can conclude that x is positive, but y could still be any value. Hence, x could be, for example, 3, but we still cannot conclusively say whether or not y is positive as well. Y could be -3 for all we know.

Should be E.

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Mon Feb 16, 2009 9:26 pm

Stmt I

x^2 = y^2

|x| = |y|

Both can be positive lets say x=2 y=2 or one could be positive or other negative x=2 y=-2

INSUFF

Stmt II

x is +ve. No info on y

INSUFF

Together

x=2 y=-2 NO answer
x=2 y=2 YES answer

Hence E

Hope this helps!

Regards,
CR

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sureshbala: Master | Next Rank: 500 Posts; Posts: 319; Joined: Wed Feb 04, 2009 10:32 amFollowed by: 9 members; Location: Delhi; Thanked: 84 times

by sureshbala » Wed Feb 18, 2009 3:28 am

Statement 1: x^2 = y^2

i.e X^2 - y^2 = 0 i.e (x+y)(x-y) = 0

Hence x = y or x = -y .

So we can't conclude whether x = y or not.

Statement 2: x is positive.

clearly this alone is not sufficient.

Combining both also, we cannot conclude whether x = y or not because x could be equal to y and be positive in which case y also will positive or x could be equal to -y and be positive in which case y will negative.

Since we do not know whether y is +ve or -ve from the both the statements given, we cannot conclude.

So E

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