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Platinum GMAT: Qn

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by anantbhatia » Thu Oct 07, 2010 11:53 pm
If x and y are distinct positive integers, what is the value of x^4 - y^4?

(y^2 + x^2)(y + x)(x - y) = 240
x^y = y^x and x > y

[spoiler]Source: Platinum GMAT OA:D[/spoiler]

Not satisfied with the explanation posted there. I doubt if it is a good level qn.

PS: Post edited to correct the typo.
Last edited by anantbhatia on Fri Oct 08, 2010 12:41 am, edited 1 time in total.
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Source: — Data Sufficiency |

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by Ian Stewart » Fri Oct 08, 2010 12:28 am
anantbhatia wrote:If x and y are distinct positive integers, what is the value of x^4 - y^4?

(y2 + x2)(y + x)(x - y) = 240
xy = yx and x > y

[spoiler]Source: Platinum GMAT OA:D[/spoiler]

Not satisfied with the explanation posted there. I doubt if it is a good level qn.
Statement 1 is sufficient; if you expand the left side, you get x^4 - y^4.

Statement 2 is clearly not sufficient. Of course xy = yx; that's always true, so that isn't useful information. We already know that x and y aren't equal, so x > y only tells us that x^4 - y^4 is positive. It might be that y = 1 and x = 2, or that y = 1 and x = 3, and the value of x^4 - y^4 will be different in each case. So the answer is A unless Statement 2 has been miscopied.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by anantbhatia » Fri Oct 08, 2010 12:40 am
Sorry Ian,

Reposting:-

If x and y are distinct positive integers, what is the value of x^4 - y^4?

(y^2 + x^2)(y + x)(x - y) = 240
x^y = y^x and x > y
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by mgm » Fri Oct 08, 2010 3:35 am
I got D only after looking at the answer ,

X^Y = Y^X ==> X^4 = (Y^X/Y)^4 = Y^4*X/Y

==> X^4 - Y^4 = Y^4(1^X/Y - 1) = 0
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by deepak123gmat » Fri Oct 08, 2010 6:28 am
2) x^y = y^x and x > y

is true only for x = 4 and y=2.

If you keep on increasing values of x and y. then y^x becomes bigger than x^y.
Just input these values in x^4 - y^4 and you will get 240.
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by anantbhatia » Fri Oct 08, 2010 11:17 am
Hi all,

The basic question is:-

Using (2), is it possible to get the required result? Or is it only possible to get the result only by plugging in the values. Also, if it is the latter case, is that acceptable?
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