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# If N=(a^4)(b^3)+1. Is N odd? 1) a^4 is even 2) b^2 is odd

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If N=(a^4)(b^3)+1. Is N odd? 1) a^4 is even 2) b^2 is odd  [#permalink]

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19 May 2019, 10:33
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85% (hard)

Question Stats:

25% (01:19) correct 75% (01:05) wrong based on 53 sessions

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If $$N=(a^4)(b^3)+1$$. Is N odd?

(1) $$a^4$$ is even
(2) $$b^2$$ is odd

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Re: If N=(a^4)(b^3)+1. Is N odd? 1) a^4 is even 2) b^2 is odd  [#permalink]

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20 May 2019, 08:43
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The question needs to state that a and b are integers. Assuming that's the case, then (a^4)(b^3) will be even or odd whenever ab is, respectively, even or odd. So the question is asking "is ab+1 odd?" which is the same as asking "is ab even?".

Using Statement 1, a is even, so ab is even. Using Statement 2, b is odd, so we don't know if ab is even -- that will depend on whether a is even or odd. So the answer is A.

If, however, a and b are not necessarily integers, then the answer is E, since we can't in that case even be sure N is an integer, let alone an odd integer.
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Re: If N=(a^4)(b^3)+1. Is N odd? 1) a^4 is even 2) b^2 is odd  [#permalink]

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25 Nov 2019, 09:11
IanStewart wrote:
The question needs to state that a and b are integers. Assuming that's the case, then (a^4)(b^3) will be even or odd whenever ab is, respectively, even or odd. So the question is asking "is ab+1 odd?" which is the same as asking "is ab even?".

Using Statement 1, a is even, so ab is even. Using Statement 2, b is odd, so we don't know if ab is even -- that will depend on whether a is even or odd. So the answer is A.

If, however, a and b are not necessarily integers, then the answer is E, since we can't in that case even be sure N is an integer, let alone an odd integer.

I agree with you. However, an even number by definition must be an integer (could you give me an example of an even number who is not an integer? the definition of even number is a number of the form n=2k where k is an integer). Therefore, should be A. I think this question is confusing in the way that is written and not something GMAT would test.
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Re: If N=(a^4)(b^3)+1. Is N odd? 1) a^4 is even 2) b^2 is odd  [#permalink]

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25 Nov 2019, 23:34
If $$N=(a^4)(b^3)+1$$. Is N odd?

(1) $$a^4$$ is even
(2) $$b^2$$ is odd

(1) a^4 is even, but b is unknown. b can be rational or irrational number. Insufficient

(2) Same reasoning, a is unknown here. Insufficient

(1)+(2) b^2 is odd, still b is unknown. b can be rational or irrational number.
Insufficient

E is correct
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Re: If N=(a^4)(b^3)+1. Is N odd? 1) a^4 is even 2) b^2 is odd  [#permalink]

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26 Nov 2019, 12:44
decar96 wrote:
I agree with you. However, an even number by definition must be an integer (could you give me an example of an even number who is not an integer?

I think you've misunderstood what I was saying. When we are told that a^4 is an even integer, that does not ensure that a itself is an integer. a might be an even integer, but a might also be equal to √2, say. That is why the question needs to tell you that the unknowns are integers.
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Re: If N=(a^4)(b^3)+1. Is N odd? 1) a^4 is even 2) b^2 is odd   [#permalink] 26 Nov 2019, 12:44
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