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# Is 3a + 2b + 5c even if 0<a<b<c and a, b and c are integers?

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Is 3a + 2b + 5c even if 0<a<b<c and a, b and c are integers?  [#permalink]

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10 Oct 2018, 10:19
2
00:00

Difficulty:

55% (hard)

Question Stats:

74% (02:11) correct 26% (03:17) wrong based on 39 sessions

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Is 3a + 2b + 5c even if 0<a<b<c and a, b and c are integers?

(1) 9a+7c is not even
(2) $$a^3*(c-1)^2$$ is odd
Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: Is 3a + 2b + 5c even if 0<a<b<c and a, b and c are integers?  [#permalink]

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10 Oct 2018, 19:04
Is 3a + 2b + 5c even if 0<a<b<c and a, b and c are integers?

2b will always be even, so we require to know 3a+5c.

(1) 9a+7c is not even
This means one of the two a and c is even and other odd, so 3a+5c will be odd and 3a+2b+5c is odd
Ans NO
Sufficient

(2) $$a^3*(c-1)^2$$ is odd
Product of two odd numbers is odd..
So a is odd and c-1 is odd, meaning c is even
Therefore 3a+2b+5c is odd
Sufficient

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Re: Is 3a + 2b + 5c even if 0<a<b<c and a, b and c are integers?  [#permalink]

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11 Oct 2018, 00:18
rencsee wrote:
Is 3a + 2b + 5c even if 0<a<b<c and a, b and c are integers?

(1) 9a+7c is not even
(2) $$a^3*(c-1)^2$$ is odd

Question: Is 3a + 2b + 5c even ?

Since 2a is a multiple of 2 so irrespective of integer value of a, 2a will always be even so now the question remains

Question: Is 3a + 5c even ?

Which will be even if either both a and c are even or both a and c are odd so the question becomes

Question REPHRASED: Are a and c both even or both odd ?

Statement 1: 9a+7c is not even

which is true only if one of a and c is even and other is Odd hence
SUFFICIENT

Statement 2: $$a^3*(c-1)^2$$ is odd

which again mean that a is Odd and c is Even hence
SUFFICIENT

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Re: Is 3a + 2b + 5c even if 0<a<b<c and a, b and c are integers?   [#permalink] 11 Oct 2018, 00:18
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