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# If n is positive integer, is 21 a factor of n?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6639
GMAT 1: 760 Q51 V42
GPA: 3.82
If n is positive integer, is 21 a factor of n?  [#permalink]

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03 Jul 2018, 00:50
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Difficulty:

35% (medium)

Question Stats:

63% (00:59) correct 37% (01:48) wrong based on 47 sessions

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[GMAT math practice question]

If $$n$$ is positive integer, is $$21$$ a factor of $$n$$?

1) $$21$$ is a factor of $$3n$$
2) $$21$$ is a factor of $$n^2$$

_________________

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 $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 04 Aug 2010 Posts: 310 Schools: Dartmouth College Re: If n is positive integer, is 21 a factor of n? [#permalink] ### Show Tags 03 Jul 2018, 03:03 MathRevolution wrote: [GMAT math practice question] If $$n$$ is positive integer, is $$21$$ a factor of $$n$$? 1) $$21$$ is a factor of $$3n$$ 2) $$21$$ is a factor of $$n^2$$ Statement 1: In other words, 3n is a multiple of 21: 3n = 21, 42, 63... To get a list of options for n, divide every value above by 3: n = 7, 14, 21... If n=7, then the answer to the question stem is NO. If n=21, then the answer to the question stem is YES. INSUFFICIENT. Statement 2: Since n is a positive integer, n² must be a perfect square that is divisible by 21: n² = 21², (2*21)², (3*21)².... n² = 21², 42², 63².... To get a list of options for n, take the square root of every value above: n = 21, 42, 63... In every case, n is divisible by 21, so the answer to the question stem is YES. SUFFICIENT. _________________ GMAT and GRE Tutor Over 1800 followers Click here to learn more GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6639 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If n is positive integer, is 21 a factor of n? [#permalink] ### Show Tags 04 Jul 2018, 23:46 => 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. Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first. Condition 1) If $$n = 21$$, then $$21$$ is a factor of n and the answer is “yes”. If $$n = 7$$, then $$21$$ is not a factor of n and the answer is “no”. Since the solution is not unique, condition 1) is not sufficient. Condition 2) Since $$21 = 3*7$$ is a factor of $$n^2$$, each of $$3$$ and $$7$$ is a factor of $$n^2$$. If $$3$$ is a factor of $$n^2$$, then, since $$3$$ is a prime number, $$3$$ is a factor of $$n$$. If $$7$$ is a factor of $$n^2$$, then, since $$7$$ is a prime number, $$7$$ is a factor of $$n$$. Thus, $$21$$ is a factor of $$n$$. Condition 2) is sufficient. Therefore, B is the answer. Answer: B If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E. _________________ 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$99 for 3 month Online Course"
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Re: If n is positive integer, is 21 a factor of n? &nbs [#permalink] 04 Jul 2018, 23:46
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# If n is positive integer, is 21 a factor of n?

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