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# M04 #02

Author Message
Senior Manager
Status: Happy to join ROSS!
Joined: 29 Sep 2010
Posts: 279
Concentration: General Management, Strategy
Schools: Ross '14 (M)
Followers: 19

Kudos [?]: 114 [0], given: 48

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21 Nov 2010, 06:37
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.
==========
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?
Math Expert
Joined: 02 Sep 2009
Posts: 33489
Followers: 5925

Kudos [?]: 73350 [2] , given: 9902

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21 Nov 2010, 06:46
2
KUDOS
Expert's post
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.
==========
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.

For more on number properties check: math-number-theory-88376.html

Hope it helps.
_________________
Senior Manager
Status: Happy to join ROSS!
Joined: 29 Sep 2010
Posts: 279
Concentration: General Management, Strategy
Schools: Ross '14 (M)
Followers: 19

Kudos [?]: 114 [0], given: 48

### Show Tags

21 Nov 2010, 07:07
Ok, so ZERO is an even number or, more precisely, ZERO IS AN EVEN INTEGER.
That explains the question.
Thanks!
Re: M04 #02   [#permalink] 21 Nov 2010, 07:07
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# M04 #02

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