Vorskl wrote:

Q: Is integer N even?

1. N^2 = N

2. N^3 = N

OA:

Statement (1) by itself is insufficient.

Statement (2) by itself is insufficient.

Statements (1) and (2) combined are insufficient. We know from S1 that the value of can be either 0 or 1. From S2, we have 1,0,-1 as possible values of . Combining the two statements does not tell us if is an even integer.

The correct answer is E.

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Why is not D? From both statements we know that N could be 0 or 1. We don't care which one exactly as long as N is not 2. Or, shall I assume that in GMAT tests ZERO is an even number?

Zero is an even integer. An even number is an

integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder.

An even number is an

integer of the form \(n=2k\), where \(k\) is an integer.

So for \(k=0\) --> \(n=2*0=0\).

As for the question:

Is integer N even?

(1) N^2 = N --> \(n(n-1)=0\) --> either \(n=0=even\) or \(n=1=odd\). Not sufficient.

(2) N^3 = N --> \(n(n-1)(n+1)=0\) --> \(n=0=even\) or \(n=1=odd\) or \(n=-1=odd\). Not sufficient.

(1)+(2) \(n\) can still be zero, so even or 1, so odd. Not sufficient.

Answer: E.

For more on number properties check:

math-number-theory-88376.htmlHope it helps.

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