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If a is an even integer

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If a is an even integer [#permalink] New post 07 Nov 2012, 21:39
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Question Stats:

89% (01:29) correct 11% (00:11) wrong based on 57 sessions
If a is an even integer and b is an odd integer which of the following must be an odd integer :

A. a/b
B. ab
C. 2a+b
D. 2(a+b)
E. 3a/b
[Reveal] Spoiler: OA

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Re: If a is an even integer [#permalink] New post 08 Nov 2012, 00:43
Pansi wrote:
If a is an even integer and b is an odd integer which of the following must be an odd integer :

A. a/b
B. ab
C. 2a+b
D. 2(a+b)
E. 3a/b


We can always look for low hanging fruits first to solve such questions under 30secs.

Expression in C, is basically 2*Even+Odd or simply Even+Odd which is always going to be odd.

Hence C it is.
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Re: If a is an even integer [#permalink] New post 19 Dec 2012, 05:58
Best option is to plug values for a and b:

Let, a=2 and b=5

Option A = 2/5 which not an integer, eliminate.

Option B = 2x5 = 10 which is even, eliminate.

Option C = 2x2+5 = 9 Possible!

Option D = 2x(2+5) = 18, eliminate

Option E = 3x2/5 = 6/5, eliminate

Answer is B.
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Re: If a is an even integer [#permalink] New post 19 Dec 2012, 08:05
Pansi wrote:
If a is an even integer and b is an odd integer which of the following must be an odd integer :

A. a/b
B. ab
C. 2a+b
D. 2(a+b)
E. 3a/b


I will take this question as an excuse to point out some things to take care in these types of questions.

1. The language:
This question asks for "must be" which means that one of the expressions has to be odd in all cases. This is especially something to take care of when you are solving by substitution, when you might find 2 options to be true. There can be other cases like "can be" or "cannot be". In these cases, you can be almost 100% be sure that in most substitution cases there can be more than 1 option that will solve to true. So make sure you use 2 cases and solve all options.

2. Even-odd combination tables.
Just remember these. If you can't, understand the logic and draw this on your scratch pad. It will be very useful when using process of elimination to arrive at the answer.
A. Addition/Subtraction (If different combine, then result is odd)
E + E = E
E + O = O
O + O = E

B. Multiplication (If one of them is even, result is even)
E * E= E
E * O = E
O * O = O
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Re: If a is an even integer   [#permalink] 19 Dec 2012, 08:05
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