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# If p is a prime number and n is a positive integer, what is the number

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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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If p is a prime number and n is a positive integer, what is the number [#permalink]

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Updated on: 03 Jan 2018, 12:37
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[GMAT math practice question]

If $$p$$ is a prime number and $$n$$ is a positive integer, what is the number of positive factors of $$3^np^2$$?

1) $$n=3$$
2) $$p$$ is odd.
[Reveal] Spoiler: OA

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"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" Originally posted by MathRevolution on 03 Jan 2018, 01:39. Last edited by MathRevolution on 03 Jan 2018, 12:37, edited 1 time in total. Intern Joined: 07 Oct 2017 Posts: 42 Re: If p is a prime number and n is a positive integer, what is the number [#permalink] ### Show Tags 03 Jan 2018, 03:02 Total factors =(2+1)(n+1) We need value of n St1: sufficient St2: no info about n Insufficient Imo A Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app PS Forum Moderator Joined: 25 Feb 2013 Posts: 1056 Location: India GPA: 3.82 Re: If p is a prime number and n is a positive integer, what is the number [#permalink] ### Show Tags 03 Jan 2018, 03:19 MathRevolution wrote: [GMAT math practice question] If $$p$$ is a prime number and $$n$$ is a positive integer, what is the number of positive factors of $$3^np^2$$? 1) $$n=3$$ 2) $$p$$ is odd. Hi MathRevolution The answer should be E & not C Statement 1: from this we get $$3^3*p^2$$. Now if $$p=3$$, then we have $$3^3*3^2=3^5$$. Hence no of factors $$=5+1=6$$ But if $$p=5$$, then we have $$3^3*5^2$$. Hence no of factors $$=(3+1)*(2+1)=12$$. Hence Insufficient Statement 2: nothing mentioned about $$n$$. Insufficient Combining 1 & 2: we know $$p$$ is odd prime hence as explained for Statement 1, there could be multiple values. Hence Insufficient Answer: Option E Hi Bunuel Request you to provide clarity on OA? PS Forum Moderator Joined: 25 Feb 2013 Posts: 1056 Location: India GPA: 3.82 Re: If p is a prime number and n is a positive integer, what is the number [#permalink] ### Show Tags 03 Jan 2018, 03:22 sumit411 wrote: Total factors =(2+1)(n+1) We need value of n St1: sufficient St2: no info about n Insufficient Imo A Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app Hi sumit411 if both the prime numbers are different then A will be the answer but if p=3, then the number of factors will be different. Intern Joined: 20 Aug 2017 Posts: 12 Re: If p is a prime number and n is a positive integer, what is the number [#permalink] ### Show Tags 03 Jan 2018, 11:45 Can you explain the OA. I think its OA is A. PS Forum Moderator Joined: 25 Feb 2013 Posts: 1056 Location: India GPA: 3.82 Re: If p is a prime number and n is a positive integer, what is the number [#permalink] ### Show Tags 04 Jan 2018, 00:00 sghoshgt wrote: Can you explain the OA. I think its OA is A. hi @sghoshgt Statement 1 does not provide the value of p. If p=3, then number of factors will be different than when p is any other prime. Hence Option A will not be sufficient here. Sent from my iPhone using GMAT Club Forum mobile app Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5268 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: If p is a prime number and n is a positive integer, what is the number [#permalink] ### Show Tags 05 Jan 2018, 00:51 => 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. Usually, when we encounter questions about numbers of factors and are given a prime factorization, the primes in the prime factorization are different. If $$p ≠ 3$$, the number of factors is $$(n+2)(2+2)$$, which can be determined from n. However, since the question gives no restrictions on p, we should consider the following two cases: Conditions 1) and 2) together: Case 1: $$p ≠ 3, n = 3$$: The number of factors is $$(3+1)(2+1) = 12$$. Case 2: $$p = 3, n = 3$$ $$3^nP^2 = 3^33^2 = 3^5$$ The number of factors is $$5+1 = 6.$$ Since we do not obtain a unique answer, both conditions together are not sufficient. Therefore, the answer is E. Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E. Answer: C _________________ 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: If p is a prime number and n is a positive integer, what is the number   [#permalink] 05 Jan 2018, 00:51
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