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cannot be even?

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by sanju09 » Tue Feb 21, 2012 4:41 am
If a and b are integers and a + 3 b is odd, which of the following cannot be even?
A. 3 a + 2 b
B. 2 a + b
C. a + 2 b
D. a + b
E. b - a b


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by Anurag@Gurome » Tue Feb 21, 2012 4:51 am
sanju09 wrote:If a and b are integers and a + 3 b is odd, which of the following cannot be even?
A. 3 a + 2 b
B. 2 a + b
C. a + 2 b
D. a + b
E. b - a b

[spoiler]made up by Sanjeev K Saxena for Avenues Abroad[/spoiler]
a + 3b = odd implies a = even, b = odd OR a = odd, b = even

Case 1: a = even, b = odd
A. 3 a + 2 b = even + even = even
B. 2 a + b = even + odd = odd
C. a + 2 b = even + even = even
D. a + b = even + odd = odd
E. b - a b = odd - even = odd

Case 2: a = odd, b = even
A. 3 a + 2 b = odd + even = odd
B. 2 a + b = even + even = even
C. a + 2 b = odd + even = odd
D. a + b = even + odd = odd
E. b - a b = even - even = even

In both cases, D is the only option, which is odd.

The correct answer is D.
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