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# Is integer N even? 1) N^2=N 2)N=N^3 Statement (1) ALONE is

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Is integer N even? 1) N^2=N 2)N=N^3 Statement (1) ALONE is [#permalink]  17 Feb 2011, 13:33
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55% (hard)

Question Stats:

60% (01:20) correct 40% (00:45) wrong based on 10 sessions
Quote:
Is integer N even?
1) N^2=N
2)N=N^3

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient
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.

Test 4, Question 2:

The question asks to find out if from the 1 or 2 we can tell that N is even.
my logic if the only numbers that fit into 1 or 2 are -1,0,1 = I can determine that N is not even> I have enough info to state if it is even or not.

what is the logics behind the answer provided?
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Re: Test 4, Question 2: if even or not [#permalink]  17 Feb 2011, 13:36
Expert's post
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.
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Re: Test 4, Question 2: if even or not [#permalink]  17 Feb 2011, 13:53
thx,
did not know that 0 is even
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Re: Test 4, Question 2: if even or not [#permalink]  18 Feb 2011, 04:01
Lombards wrote:
Quote:
Is integer N even?
1) N^2=N
2)N=N^3

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient
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.

Test 4, Question 2:

The question asks to find out if from the 1 or 2 we can tell that N is even.
my logic if the only numbers that fit into 1 or 2 are -1,0,1 = I can determine that N is not even> I have enough info to state if it is even or not.

what is the logics behind the answer provided?

Statement 1: N^2= N. There are 2 numbers that satisfy this condition: 0, 1. Zero is even. 1 is odd. two different answers. Insufficient.

Statement 2: N^3= N: There are 3 numbers that satisfy this condition: 0, 1 and -1. 0 is even, 1 and -1 are odd.. Impossible to determine which one to pick. Insufficient.

1&2, No new information can be obtained by combining the sentences. Insufficient.

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Re: Test 4, Question 2: if even or not   [#permalink] 18 Feb 2011, 04:01
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