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# If a and b are odd natural numbers, is 7/2 + a/2 + b/3 an integer?

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If a and b are odd natural numbers, is 7/2 + a/2 + b/3 an integer? [#permalink]

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04 Aug 2017, 08:21
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Difficulty:

55% (hard)

Question Stats:

40% (00:26) correct 60% (01:05) wrong based on 30 sessions

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If a and b are odd natural numbers, is $$\frac{7}{2} + \frac{a}{2} + \frac{b}{3}$$ an integer?

(1) a is a multiple of 3

(2) b is a multiple of 3
[Reveal] Spoiler: OA

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Re: If a and b are odd natural numbers, is 7/2 + a/2 + b/3 an integer? [#permalink]

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04 Aug 2017, 08:43
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Expert's post
7/2 + a/2 + b/3 = (7 + a)/2 + b/3

If a is odd, 7 + a is even, so 7 + a is divisible by 2, and (7 + a)/2 is an integer. So we're adding some integer to b/3, and if we want this sum to be an integer, b/3 will need to be an integer, so b will need to be divisible by 3. Statement 2 guarantees that, but Statement 1 does not, so the answer is B.
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Re: If a and b are odd natural numbers, is 7/2 + a/2 + b/3 an integer?   [#permalink] 04 Aug 2017, 08:43
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