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x^3 – x^2 is a square

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x^3 – x^2 is a square

by Brent@GMATPrepNow » Sat Jan 31, 2009 4:09 pm
If x is an integer greater than 1, and x^3 – x^2 is a square, then what is the value of x?

(1) x is a divisor of 36
(2) x is a divisor of 30
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by vikram_k51 » Sat Jan 31, 2009 4:23 pm
If x is an integer greater than 1, and x^3 – x^2 is a square, then what is the value of x?

(1) x is a divisor of 36
(2) x is a divisor of 30


Question Rephrase: Is x^2(x-1) a square?
Or Is x-1 a square?

For x-1 to be a square the possible x are:2,5,10,17,26,37 etc

From 1: x is a divisor of 36.Which is satisfied byx=2 only.Hence sufficient.

From 2: x is a divisor of 30;3 values qualify:2,5,10;Not Sufficient.

Hence A
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by Brent@GMATPrepNow » Sat Jan 31, 2009 4:27 pm
Great work, vikram_k51
The answer is A
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