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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8001
GMAT 1: 760 Q51 V42 GPA: 3.82

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Difficulty:   45% (medium)

Question Stats: 40% (00:55) correct 60% (01:13) wrong based on 10 sessions

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If $$x$$ and $$y$$ are integers, is $$x^2+11x+13y$$ an even number?

1) $$x=11$$

2) $$y=13$$

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8001
GMAT 1: 760 Q51 V42 GPA: 3.82

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Official Solution:

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, and then recheck the question.

Now, $$x^2+11x+13y = x(x+11)+13y$$. As $$x(x+11)$$ is always an even integer (one of $$x$$ and $$x + 11$$ must be even), $$x^2+11x+13y$$ is even precisely when $$13y$$ is even. This is equivalent to $$y$$ being even, so the question can be restated as 'Is $$y$$ an even number?

Condition 1)

If $$x = 11$$ and $$y = 1$$, then $$x^2+11x+13y = 255$$ is an odd integer.

If $$x = 11$$ and $$y = 2$$, then $$x^2+11x+13y = 268$$ is an even integer.

Since the question does not have a unique answer, condition 1) is not sufficient.

Condition 2)

If $$y = 13$$, then $$y$$ is odd, and the answer to the question is 'no'.

Condition 2) is sufficient.

Therefore, B is the answer.

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Intern  B
Joined: 24 Sep 2017
Posts: 1

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In this question, option D can also be selected as a correct answer. Since by taking values of both statements a definitive answer of the question can be obtained.
Intern  Joined: 18 Nov 2014
Posts: 12

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I think this is a high-quality question and I agree with explanation. different and good approach to solve the question
Intern  B
Joined: 25 Feb 2019
Posts: 1

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I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. i don't understand the solution especially when both statements were involved in arriving at the answer, why is C wrong Re M60-24   [#permalink] 29 Apr 2019, 16:52
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