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# For the integers x and y, if xy is a multiple of 25, is y a multiple o

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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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For the integers x and y, if xy is a multiple of 25, is y a multiple o [#permalink]

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02 Mar 2018, 01:17
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35% (medium)

Question Stats:

69% (01:03) correct 31% (01:14) wrong based on 39 sessions

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[GMAT math practice question]

For the integers $$x$$ and $$y$$, if $$xy$$ is a multiple of $$25$$, is $$y$$ a multiple of $$5$$?

1) $$x-y$$ is a multiple of $$5$$
2) $$x$$ is a multiple of $$2$$
[Reveal] Spoiler: OA

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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" DS Forum Moderator Joined: 22 Aug 2013 Posts: 884 Location: India Re: For the integers x and y, if xy is a multiple of 25, is y a multiple o [#permalink] ### Show Tags 02 Mar 2018, 02:54 1 This post was BOOKMARKED MathRevolution wrote: [GMAT math practice question] For the integers $$x$$ and $$y$$, if $$xy$$ is a multiple of $$25$$, is $$y$$ a multiple of $$5$$? 1) $$x-y$$ is a multiple of $$5$$ 2) $$x$$ is a multiple of $$2$$ x*y is a multiple of 25, which is 5^2. This means Either both x and y have at least one '5' each in their prime factorisation, Or its also possible that one of x/y does not have any '5' and the other one of x/y has at least two 5's in its prime factorisation. (then only x*y will be a multiple of 5^2) Also if sum (or difference) of two integers is a multiple of 5, then Either each one of them is a multiple of 5 Or none of the two integers is a multiple of 5. (1) x-y is a multiple of 5, so either each of them is a multiple of 5 Or none of the two integers is a multiple of 5. But the latter case is Not possible here since x*y is divisible by 5^2. So it means each of x/y must have at least one 5, so 'y' is a multiple of 5. Sufficient. (2) x is a multiple of 2, this doesn't tell anything about divisibility by 5 of y. Not sufficient. Hence A answer Intern Joined: 15 Mar 2017 Posts: 44 Location: India Concentration: International Business, Strategy Schools: Kellogg '20 GMAT 1: 720 Q50 V37 GPA: 4 Re: For the integers x and y, if xy is a multiple of 25, is y a multiple o [#permalink] ### Show Tags 03 Mar 2018, 01:39 1 This post received KUDOS Given: x times y is a multiple of 25, 2 scenarios : Both x and y Are multiple of 5 b) Either x or y is a multiple of 25 Statement 1: (1) x-y is a multiple of 5. Either each of them is a multiple of 5 or none of the two integers is a multiple of 5. 2nd case is out of consideration. SUFFICIENT. (2) x is a multiple of 2, but is X a multiple of 10 or 25. We dont know. INUFFICIENT _________________ You give kudos, you get kudos. :D Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5034 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: For the integers x and y, if xy is a multiple of 25, is y a multiple o [#permalink] ### Show Tags 04 Mar 2018, 19:24 => 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. Since $$xy = 25 =5^2$$, $$x$$ is a multiple of $$5$$ or $$y$$ is a multiple of $$5$$. If $$x$$ is a multiple of $$5$$, $$y = x – 5$$ is also a multiple of $$5$$. Thus the condition 1) is sufficient. Condition 2) Since we don’t have any information from the condition 2), it is not sufficient. Therefore, A is the answer. Answer: A _________________ 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: For the integers x and y, if xy is a multiple of 25, is y a multiple o   [#permalink] 04 Mar 2018, 19:24
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