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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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GMAT 1: 800 Q59 V59
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If x and y are integers, is x^2+11x+13y an even number? [#permalink]

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08 Feb 2018, 01:11
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[GMAT math practice question]

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

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

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 5779 Re: If x and y are integers, is x^2+11x+13y an even number? [#permalink] ### Show Tags 08 Feb 2018, 03:09 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.. Nothing about y.. Insufficient II. y=13 So ans is Odd.. Suff B _________________ Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html GMAT online Tutor Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5437 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: If x and y are integers, is x^2+11x+13y an even number? [#permalink] ### Show Tags 11 Feb 2018, 17:54 => 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. Therefore, B is the answer. Answer: B _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 3 month Online Course"
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Re: If x and y are integers, is x^2+11x+13y an even number?   [#permalink] 11 Feb 2018, 17:54
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