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Tricky question - how squares and cubes relate

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Source: — Data Sufficiency |
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by cramya » Thu Nov 06, 2008 6:05 am
I would go with E)


Stmt I INSUFF

2 ^ 2 = 4(EVEN)
3 ^ 2 = 9(ODD)

Stmt II INSUFF

2 ^ 3 = 8(even)
3 ^ 3 = 27(odd)

Stmt I and Stmt II put together still INSUFF

0 ^ 2 = 0 0 ^ 3 = 0 (EVEN)

1 ^ 2 = 1 1 ^ 3 = 1 (ODD)

INSUFF



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icky question - how squares and cubes relate

by kumarkams » Thu Nov 06, 2008 1:25 pm
I believe we should go one step further. If we combine both statements, we can say that X is square of an integer as well as cube of an integer. We can have two values of X; 0 and 1. As both of these are integers, we can't determine a unique value of X and hence answer should be E.
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Re: icky question - how squares and cubes relate

by Ian Stewart » Thu Nov 06, 2008 2:16 pm
kumarkams wrote:I believe we should go one step further. If we combine both statements, we can say that X is square of an integer as well as cube of an integer. We can have two values of X; 0 and 1. As both of these are integers, we can't determine a unique value of X and hence answer should be E.
The examples of 0 and 1 are certainly enough to prove that the answer is E, but we can have many different values of x here - not only 0 and 1. Indeed, any sixth power will do. For example, if x = 2^6 = 64, then x is the square of an integer (x = 8^2), and x is also the cube of an integer (x = 4^3). You could equally let x = 3^6, or 4^6, and so on.
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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