It is currently 23 Jan 2018, 12:10

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4715
GPA: 3.82
If p is a prime number and n is a positive integer, what is the number [#permalink]

### Show Tags

03 Jan 2018, 00:39
1
KUDOS
Expert's post
00:00

Difficulty:

95% (hard)

Question Stats:

26% (01:10) correct 74% (00:46) wrong based on 69 sessions

### HideShow timer Statistics

[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

_________________

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.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

Last edited by MathRevolution on 03 Jan 2018, 11:37, edited 1 time in total.
Intern
Joined: 07 Oct 2017
Posts: 43
Re: If p is a prime number and n is a positive integer, what is the number [#permalink]

### Show Tags

03 Jan 2018, 02:02
Total factors =(2+1)(n+1)
We need value of n

St1: sufficient
Insufficient

Imo A

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 838
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, 02:19
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

Hi Bunuel

Request you to provide clarity on OA?
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 838
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, 02:22
sumit411 wrote:
Total factors =(2+1)(n+1)
We need value of n

St1: sufficient
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: 4
Re: If p is a prime number and n is a positive integer, what is the number [#permalink]

### Show Tags

03 Jan 2018, 10:45
Can you explain the OA. I think its OA is A.
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 838
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, 23:00
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: 4715
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, 23:51
=>

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.

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.

_________________

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.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

Re: If p is a prime number and n is a positive integer, what is the number   [#permalink] 04 Jan 2018, 23:51
Display posts from previous: Sort by