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DS-integer sq/cube

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by anjaneiya » Wed Dec 08, 2010 6:32 am
If X is an integer, what is the value of X ?

1. X^2 = X^3

2. X is both a perfect square and a perfect cube.

Note: A perfect square is a number that has a whole number as its square root.

pl explain....thanks.
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Source: — Data Sufficiency |

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by Rahul@gurome » Wed Dec 08, 2010 7:47 am
anjaneiya wrote:If X is an integer, what is the value of X ?
1. X^2 = X^3
2. X is both a perfect square and a perfect cube.
Statement 1: x² = x³
.... x³ = x²
=> (x³ - x²) = 0
=> x²(x - 1) = 0

Either x = 0 or x = 1.

Not sufficient.

Statement 2: x is both a perfect square and a perfect cube
x may be 0 or 1 or 64 etc. In general any integer of the form n^6, where n is any integer.

Not sufficient.

1 & 2 Together: Still possible values of x are 0 and 1.

Not sufficient.

The correct answer is E.
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by anjaneiya » Thu Dec 09, 2010 4:02 am
thanks rahul..!!!
i was not sure about is 0 isto be consider as sq and/or cube.
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