GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 18 Jul 2018, 12:53

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
2 KUDOS received
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 5846
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
If p is a prime number and n is a positive integer, what is the number [#permalink]

Show Tags

New post Updated on: 03 Jan 2018, 12:37
2
1
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

33% (01:04) correct 67% (00:52) wrong based on 89 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.

_________________

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"
"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
Intern
avatar
B
Joined: 07 Oct 2017
Posts: 44
Re: If p is a prime number and n is a positive integer, what is the number [#permalink]

Show Tags

New post 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
avatar
D
Joined: 25 Feb 2013
Posts: 1182
Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge
Re: If p is a prime number and n is a positive integer, what is the number [#permalink]

Show Tags

New post 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
avatar
D
Joined: 25 Feb 2013
Posts: 1182
Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge
Re: If p is a prime number and n is a positive integer, what is the number [#permalink]

Show Tags

New post 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
Intern
avatar
B
Joined: 20 Aug 2017
Posts: 17
Re: If p is a prime number and n is a positive integer, what is the number [#permalink]

Show Tags

New post 03 Jan 2018, 11:45
Can you explain the OA. I think its OA is A.
PS Forum Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1182
Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge
Re: If p is a prime number and n is a positive integer, what is the number [#permalink]

Show Tags

New post 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
Expert Post
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 5846
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: If p is a prime number and n is a positive integer, what is the number [#permalink]

Show Tags

New post 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 $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"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] 05 Jan 2018, 00:51
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


cron

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.