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If n is a positive integer, is n^2+2n+44 divisible by 4?

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by Max@Math Revolution » Sun May 12, 2019 11:29 pm

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[GMAT math practice question]

If n is a positive integer, is n^2+2n+44 divisible by 4?

1) n is an even integer.
2) n^2 is divisible by 144
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Source: — Data Sufficiency |
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by Max@Math Revolution » Tue May 14, 2019 11:23 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.

Asking if "n^2+2n+44 is divisible by 4" is equivalent to asking if n is an even integer, since 44 is a multiple of 4 and n^2+2n = n(n+2) is a multiple of 4 when n is an even number.
Thus, condition 1) is sufficient.

Condition 2)
Since n^2 is divisible by 144, n is divisible by 12 and n is an even number.
Thus, condition 2) is also sufficient.

Therefore, D is the answer.
Answer: D

Note: Tip 1) of the VA method states that D is most likely to be the answer if condition 1) gives the same information as condition 2).
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