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# If n is positive integer, is 35 a factor of n?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6616
GMAT 1: 760 Q51 V42
GPA: 3.82
If n is positive integer, is 35 a factor of n?  [#permalink]

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20 Jul 2018, 00:25
00:00

Difficulty:

25% (medium)

Question Stats:

67% (00:58) correct 33% (01:00) wrong based on 48 sessions

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[GMAT math practice question]

If $$n$$ is positive integer, is $$35$$ a factor of $$n$$?

1) $$35$$ is a factor of $$n^2$$
2) $$35$$ is a factor of $$5n$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"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" Director Joined: 20 Feb 2015 Posts: 796 Concentration: Strategy, General Management Re: If n is positive integer, is 35 a factor of n? [#permalink] ### Show Tags 20 Jul 2018, 01:42 MathRevolution wrote: [GMAT math practice question] If $$n$$ is positive integer, is $$35$$ a factor of $$n$$? 1) $$35$$ is a factor of $$n^2$$ 2) $$35$$ is a factor of $$5n$$ 1. 35 is a factor of n^2 35=7*5 n^2=5*7*p n=root5*7*p since n is a positive integer the root must have atleast another set of 5 and 7 in it therefore n=35*p sufficient 2. 35 is a factor of 5n 35=7*5 5n=7*5*q n=7q now q can be any value not necessarily 5 insufficient A Senior Manager Joined: 29 Dec 2017 Posts: 385 Location: United States Concentration: Marketing, Technology GMAT 1: 630 Q44 V33 GMAT 2: 690 Q47 V37 GMAT 3: 710 Q50 V37 GPA: 3.25 WE: Marketing (Telecommunications) Re: If n is positive integer, is 35 a factor of n? [#permalink] ### Show Tags 20 Jul 2018, 08:36 If $$n$$ is positive integer, is $$35$$ a factor of $$n$$? 1) $$35$$ is a factor of $$n^2$$ - there is a rule to remember n and n^2 will always have the same prime factors 2) $$35$$ is a factor of $$5n$$ - clearly NS Answer A. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6616 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If n is positive integer, is 35 a factor of n? [#permalink] ### Show Tags 22 Jul 2018, 17:15 => 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) Since 35=5*7 is a factor of $$n^2$$, 5 and 7 are factors of $$n^2$$. Since 5 and 7 are prime integers and n2 is divisible by 5 and 7, n is divisible by both 5 and 7. Thus, 35 is a factor of n. Condition 1) is sufficient. Condition 2) If n = 35, then 35 is a factor of n. If n = 7, then 35 is not a factor of n. Since we don’t have a unique answer, condition 2) is not sufficient. Therefore, A is the answer. Answer: A 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 35 a factor of n? &nbs [#permalink] 22 Jul 2018, 17:15
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