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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42 GPA: 3.82
If p is a prime number and n is a positive integer, what is the number  [#permalink]

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Question Stats: 38% (01:38) correct 62% (01:15) wrong based on 95 sessions

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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.

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

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Total factors =(2+1)(n+1)
We need value of n

St1: sufficient
St2: no info about n
Insufficient

Imo A

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

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1
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

Hi Bunuel

Request you to provide clarity on OA?
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Re: If p is a prime number and n is a positive integer, what is the number  [#permalink]

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

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Can you explain the OA. I think its OA is A.
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Re: If p is a prime number and n is a positive integer, what is the number  [#permalink]

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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.

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Math Revolution GMAT Instructor V
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GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If p is a prime number and n is a positive integer, what is the number  [#permalink]

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=>

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.

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

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_________________ Re: If p is a prime number and n is a positive integer, what is the number   [#permalink] 27 Jun 2019, 11:50
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