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# What is the number of factors of a positive integer n?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8583
GMAT 1: 760 Q51 V42
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What is the number of factors of a positive integer n?  [#permalink]

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27 Feb 2018, 00:53
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Difficulty:

25% (medium)

Question Stats:

63% (00:39) correct 37% (00:43) wrong based on 109 sessions

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[GMAT math practice question]

What is the number of factors of a positive integer $$n$$?

1) $$n$$ is a multiple of $$7$$
2) $$n$$ is a prime number

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Current Student Joined: 07 Jan 2016 Posts: 1080 Location: India GMAT 1: 710 Q49 V36 Re: What is the number of factors of a positive integer n? [#permalink] ### Show Tags 27 Feb 2018, 00:57 MathRevolution wrote: [GMAT math practice question] What is the number of factors of a positive integer $$n$$? 1) $$n$$ is a multiple of $$7$$ 2) $$n$$ is a prime number 1) n is a multiple of 7 n can be 7 14 21 and each number has different factors insufficient 2) n is prime we know prime number has 2 factors i.e 1 and itself sufficient (B) imo GMAT Club Legend Joined: 11 Sep 2015 Posts: 4337 Location: Canada Re: What is the number of factors of a positive integer n? [#permalink] ### Show Tags 27 Feb 2018, 07:22 Top Contributor MathRevolution wrote: [GMAT math practice question] What is the number of factors of a positive integer $$n$$? 1) $$n$$ is a multiple of $$7$$ 2) $$n$$ is a prime number Target question: What is the number of factors of a positive integer n? Statement 1: n is a multiple of 7 There are several values of n that satisfy statement 1. Here are two: Case a: n = 7. In this case, n has TWO factors (1 and 7) Case b: n = 14. In this case, n has FOUR factors (1, 2, 7 and 14) Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: n is a prime number ALL prime numbers have exactly TWO factors. So, if n is a prime number, then the TWO factors are 1 and n In other words, n has exactly TWO factors Since we can answer the target question with certainty, statement 2 is SUFFICIENT Answer: B RELATED VIDEO _________________ Test confidently with gmatprepnow.com Manager Joined: 23 Sep 2016 Posts: 230 Re: What is the number of factors of a positive integer n? [#permalink] ### Show Tags 28 Feb 2018, 22:45 MathRevolution wrote: [GMAT math practice question] What is the number of factors of a positive integer $$n$$? 1) $$n$$ is a multiple of $$7$$ 2) $$n$$ is a prime number solution IMO B statement 1 n is a multiple of 7 then n can be 7 or 14 or 70 so this answer is insufficient statement 2 tell us its a prime number then it must have 2 factors from its definition 1 and its self so B is sufficient because question just ask about no. of factors not what is n. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8583 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the number of factors of a positive integer n? [#permalink] ### Show Tags 01 Mar 2018, 02:43 => 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) $$n = 7$$ : The number of factors of n is $$2$$. $$n = 14$$ : The number of factors of n is $$4$$. Since the answer is not unique, condition 1) is not sufficient. Condition 2) $$n = p^1$$, where p is a prime number. The number of factors on n is $$1 + 1 = 2.$$ Thus, condition 2) is sufficient. Therefore, the answer is B. 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$79 for 1 month Online Course"
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Re: What is the number of factors of a positive integer n?   [#permalink] 01 Mar 2018, 02:43
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