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vineetbatra: Master | Next Rank: 500 Posts; Posts: 355; Joined: Thu Feb 19, 2009 12:42 pmFollowed by: 1 member; Thanked: 2 times

by vineetbatra » Mon Jun 01, 2009 3:58 am

Id X^2 - Y^2 a positive number?

1. X- Y is a positive number

2. X + Y is a positive number

Answer is C.

Not sure how to get there.

Thanks,

Vineet

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Source: Beat The GMAT — Problem Solving | Mon Jun 01, 2009 3:58 am

mike22629: Master | Next Rank: 500 Posts; Posts: 322; Joined: Fri Mar 27, 2009 3:56 pm; Thanked: 24 times; GMAT Score:710

by mike22629 » Mon Jun 01, 2009 5:00 am

This is somewhat of a tricky question:

First thing you should always do with DS is to factor information in answer:

So:
Is x^2>y^2
x^2 - y^2 = (x+y)(x-y)

Now, at first glance you might think that the answer is A, because x-y>0 essentially means that x>y. And if x >y, then x^2 must be greater than y^2 right? Well the answer is not necessarily because x and y could both be fractions.

B is insufficient on its own.

But together, if x+y>0 and x-y>0, then x^2-y^2 must be greater than 0 because it is the product of (x+y)(x-y). Because they are both positive, the answer must be positive.

C is answer.

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vineetbatra: Master | Next Rank: 500 Posts; Posts: 355; Joined: Thu Feb 19, 2009 12:42 pmFollowed by: 1 member; Thanked: 2 times

Thanks

by vineetbatra » Mon Jun 01, 2009 5:06 am

Thanks Mike, when I was looking for option A i was considering negatives, i.e. -3, -4. This also brings a positive value for X-Y, but I forgot about the fractions.

Have you already got 710 in GMAT? that is a great score, how long did you take to solve this question?

Thanks,

Vineet

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mike22629: Master | Next Rank: 500 Posts; Posts: 322; Joined: Fri Mar 27, 2009 3:56 pm; Thanked: 24 times; GMAT Score:710

by mike22629 » Mon Jun 01, 2009 5:06 am

On second look, the answer is C, not A, because y could be negative.

For example, if x-y>0, x= 3, y=-4
so x-y=7

but 3^2 - (-4)^2 = -7

So really you need to find out if lxl > lyl

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mike22629: Master | Next Rank: 500 Posts; Posts: 322; Joined: Fri Mar 27, 2009 3:56 pm; Thanked: 24 times; GMAT Score:710

by mike22629 » Mon Jun 01, 2009 5:08 am

Yes I took the test on May 26th of this year, and the question took me less than a minute. With practice you will quickly learn how to solve these questions quickly.

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vineetbatra: Master | Next Rank: 500 Posts; Posts: 355; Joined: Thu Feb 19, 2009 12:42 pmFollowed by: 1 member; Thanked: 2 times

Thanks

by vineetbatra » Mon Jun 01, 2009 5:09 am

not bad at all, I still have to get into the groove.

Cheers and all the best.

Vineet

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