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If a,b and c are three positive integers such that at least one of

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Senior Manager
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Joined: 18 Feb 2019
Posts: 283
Location: India
GMAT 1: 490 Q47 V13
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If a,b and c are three positive integers such that at least one of  [#permalink]

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New post 25 Mar 2019, 09:45
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

45% (01:53) correct 55% (02:35) wrong based on 22 sessions

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If a,b, and c are three positive integers such that at least one of them is odd, which of the following statements must be true?

A. a + b + c is odd
B. a + b + c and abc have the same even-odd nature
C. 100a + 10b + c is odd
D. If b/2 and c/2 are integers, 2a+b/2+c/2 is even
E. None of the above
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Re: If a,b and c are three positive integers such that at least one of  [#permalink]

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New post 25 Mar 2019, 11:19
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Top Contributor
kiran120680 wrote:
If a,b, and c are three positive integers such that at least one of them is odd, which of the following statements must be true?

A. a + b + c is odd
B. a + b + c and abc have the same even-odd nature
C. 100a + 10b + c is odd
D. If b/2 and c/2 are integers, 2a+b/2+c/2 is even
E. None of the above


The question asks "What MUST be true?"
So, if we can show that an answer choice need not be true, we can ELIMINATE it.

A. a + b + c is odd
If a = 1, b = 2 and c = 3, then a + b + c = 1 + 2 + 3 = 6, which is NOT odd
ELIMINATE A


B. a + b + c and abc have the same even-odd nature
If a = 2, b = 2 and c = 3, then a + b + c = 2 + 2 + 3 = 7 (ODD)
If a = 2, b = 2 and c = 3, then abc = (2)(2)(3) = 12 (EVEN)
ELIMINATE B


C. 100a + 10b + c is odd
If a = 1, b = 1 and c = 2, then 100a + 10b + c = 100(1) + 10(1) + 2 = 112, which is NOT odd
ELIMINATE C


D. If b/2 and c/2 are integers, 2a + b/2 + c/2 is even
If a = 1, b = 6 and c = 4, then b/2 and c/2 are integers
However, 2a + b/2 + c/2 = 2(1) + 6/2 + 4/2 = 2 + 3 + 2 = 7, which is NOT even
ELIMINATE D

By the process of elimination, the correct answer is E

Cheers,
Brent
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Re: If a,b and c are three positive integers such that at least one of   [#permalink] 25 Mar 2019, 11:19
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