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• ### $450 Tuition Credit & Official CAT Packs FREE December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### FREE Quant Workshop by e-GMAT! December 16, 2018 December 16, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. # What is the number of factors of a positive integer n?  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6639 GMAT 1: 760 Q51 V42 GPA: 3.82 What is the number of factors of a positive integer n? [#permalink] ### Show Tags 27 Feb 2018, 00:53 00:00 Difficulty: 25% (medium) Question Stats: 63% (00:38) correct 37% (00:42) wrong based on 80 sessions ### HideShow timer Statistics [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 _________________ 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: What is the number of factors of a positive integer n?  [#permalink]

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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
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Re: What is the number of factors of a positive integer n?  [#permalink]

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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

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Re: What is the number of factors of a positive integer n?  [#permalink]

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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.
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Re: What is the number of factors of a positive integer n?  [#permalink]

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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.

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.
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Re: What is the number of factors of a positive integer n? &nbs [#permalink] 01 Mar 2018, 02:43
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