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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GPA: 3.82
If x and y are integers, is x^2+11x+13y an even number? [#permalink]

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08 Feb 2018, 00:11
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[GMAT math practice question]

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

$$1) x=11$$
$$2) y=13$$
[Reveal] Spoiler: OA

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Joined: 02 Aug 2009
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Re: If x and y are integers, is x^2+11x+13y an even number? [#permalink]

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08 Feb 2018, 02:09
MathRevolution wrote:
[GMAT math practice question]

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

$$1) x=11$$
$$2) y=13$$

$$x^2+11x$$ will be even IRRESPECTIVE of x..
If x is ODD.. O^2+11*O= O+O=E
If x is EVEN..E^2+11*E=E+E=E..

So $$x^2+11x+13y$$ depends on value of y only ..
If y is Odd, E+13*O=O
If y is Even, E+13*E=E

Let's see statement..
I. x=11..
Insufficient
II. y=13
So ans is Odd..
Suff

B
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Math Revolution GMAT Instructor
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Re: If x and y are integers, is x^2+11x+13y an even number? [#permalink]

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11 Feb 2018, 16:54
=>
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 [mx + 11[/m] 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.

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Re: If x and y are integers, is x^2+11x+13y an even number?   [#permalink] 11 Feb 2018, 16:54
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