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If a and b are positive integers, is a+b divisible by 7?

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by Max@Math Revolution » Wed Feb 20, 2019 5:18 pm

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[GMAT math practice question]

If a and b are positive integers, is a+b divisible by 7?

1) a - b is divisible by 7
2) a+b+7 is divisible by 91
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Source: — Data Sufficiency |
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by Max@Math Revolution » Thu Feb 21, 2019 10:57 pm
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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Condition 2) tells us that a + b + 7 = 91k for some integer k, and so a + b = 91k - 7 = 7(13k-1). Therefore, a + b is a multiple of 7.
Thus, condition 2) is sufficient.

Condition 1)
If a = 14 and b = 7, then a + b = 21 is a multiple of 7, and the answer is 'yes'.
If a = 8 and b = 1, then a + b = 9 is not a multiple of 7, and the answer is 'no'.
Thus, condition 1) is not sufficient since it does not yield a unique solution.

Therefore, B is the answer.
Answer: B
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