If a and b are integers, is a + 8b even? (1) 2a + b is even

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Mon Oct 12, 2015 11:00 pm

If a and b are integers, is a + 8b even?

(1) 2a + b is even

(2) a^b is even

Answer: Option B

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Source: Beat The GMAT — Data Sufficiency | Mon Oct 12, 2015 11:00 pm

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Mon Oct 12, 2015 11:00 pm

GMATinsight wrote:If a and b are integers, is a + 8b even?

(1) 2a + b is even

(2) a^b is even

Answer: Option B

Question : is a + 8b even?

Since 8b will always be an Even Integer given that a and b are Integers so we only need to know about a to answer the question

Question REPHRASED : Is a even?

Statement 1: 2a + b is even
Since 2a is always even so we conclude that b is even.
But we need to know whether a is even or not hence
NOT SUFFICIENT

Statement 2: a^b is even
i.e. a is even
SUFFICIENT

Answer: Option B

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Wed Oct 14, 2015 6:03 am

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If a and b are integers, is a + 8b even?
(1) 2a + b is even
(2) a^b is even

If we modify the original condition according to the Variable Approach Method, from a+8b, 8b is always even, so we ultimately want to know whether a is an even number.
From condition 2, in order for a^b to be even, the product of even numbers are always even, so a=even, and this condition is sufficient.
But for condition 1, 2a is always even regardless of the value of a, so we cannot determine the value of a, so this is a insufficient condition, and the answer is therefore (B).

Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.

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