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

 It is currently 19 Nov 2018, 07:44

### 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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### How to QUICKLY Solve GMAT Questions - GMAT Club Chat

November 20, 2018

November 20, 2018

09:00 AM PST

10:00 AM PST

The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
• ### The winning strategy for 700+ on the GMAT

November 20, 2018

November 20, 2018

06:00 PM EST

07:00 PM EST

What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

# 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: 6526
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]

### Show Tags

25 Jul 2018, 00:08
00:00

Difficulty:

85% (hard)

Question Stats:

26% (01:33) correct 74% (00:44) wrong based on 43 sessions

### HideShow timer Statistics

[Math Revolution GMAT math practice question]

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

1)$$n = 4$$
2) $$p > 4$$

_________________

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" MBA Section Director Affiliations: GMATClub Joined: 22 May 2017 Posts: 1005 Concentration: Nonprofit GPA: 4 WE: Engineering (Computer Software) If p is a prime number and n is a positive integer, what is the number [#permalink] ### Show Tags Updated on: 25 Jul 2018, 00:31 1 To find the number of factors of $$3^n p^2$$ Statement 1 n = 4 If p $$\neq$$ 3 then number of factors = (n + 1) * (2 + 1) = 5 * 3 = 15 If p = 3 then number of factors = n + 2 + 1 = 7 Statement 1 is not sufficient Statement 2 p > 4 number of factors of $$3^n p^2$$ = (n + 1) * (2 + 1) Since we don't know the value of n, statement 2 is insufficient Combining statements 1 and 2 p > 4 => p $$\neq$$ 3 then number of factors = (n + 1) * (2 + 1) = 5 * 3 = 15 Hence option C _________________ Originally posted by workout on 25 Jul 2018, 00:17. Last edited by workout on 25 Jul 2018, 00:31, edited 2 times in total. Senior Manager Joined: 15 Oct 2017 Posts: 312 If p is a prime number and n is a positive integer, what is the number [#permalink] ### Show Tags 25 Jul 2018, 00:27 Given: n=4, p=prime number. To know the number of factors, we need to know the powers of primes and whether p=3. 1) If p=3, then the total number of factors= 6+1 =7. But if p is not equal to 3, then the total number of factors will be (4+1)*(2+1) = 5*3 = 15. Not Sufficient. 2) If p>4, then the total number of factors = (2+1)*(n+1). But we do not know the value of n. Hence not sufficient. Combining 1 & 2, we get n=4 and p is not equal to 3. Therefore the total number of factors = (4+1)*(2+1) = 15. Sufficient. Therefore, C. Senior Manager Joined: 04 Aug 2010 Posts: 307 Schools: Dartmouth College Re: If p is a prime number and n is a positive integer, what is the number [#permalink] ### Show Tags 25 Jul 2018, 03:10 To count the factors of a positive integer: 1. Prime-factorize the integer 2. Write the prime-factorization in the form $$(a^p)(b^q)(c^r)$$... 3. The number of factors = $$(p+1)(q+1)(r+1)$$... MathRevolution wrote: [Math Revolution GMAT math practice question] If $$p$$ is a prime number and $$n$$ is a positive integer, what is the number of factors of $$3^np^2$$? 1)$$n = 4$$ 2) $$p > 4$$ Statement 1: $$n=4$$ Test one case that also satisfies Statement 2. Case 1: $$p=5$$, with the result that $$3^np^2 = (3^4)(5^2)$$ Adding 1 to each exponent and multiplying, we get: Number of factors $$= (4+1)(2+1) = 15$$ Test a case that does NOT also satisfy Statement 2. Case 1: $$p=3$$, with the result that $$3^np^2 = (3^4)(3^2) = 3^6$$ Adding 1 to the only exponent, we get: Number of factors $$= 6+1 = 7$$ Since the number of factors can be different values, INSUFFICIENT. Statement 2: $$p>4$$ Case 1 also satisfies Statement 2. In Case 1, the number of factors = 15. Case 3: $$p=5$$ and $$n=2$$, with the result that $$3^np^2 = (3^2)(5^2)$$ Adding 1 to each exponent and multiplying, we get: Number of factors $$= (2+1)(2+1) = 9$$ Since the number of factors can be different values, INSUFFICIENT. Statements combined: As illustrated by Case 1, if $$n=4$$ and $$p>4$$, the number of factors = 15. SUFFICIENT. _________________ GMAT and GRE Tutor Over 1800 followers Click here to learn more GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6526 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] ### Show Tags 26 Jul 2018, 23:49 => 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. We then recheck the question. If a question asks for a number of factors, it is very important to check that all of the given prime factors are “different”. By condition 2), $$p$$ is a prime number different from $$3$$. To determine the number of factors, we need to know the exponents in the prime number factorization. Therefore, we also need condition 1). Since $$p$$ is a different prime integer from $$3$$, and $$n = 4$$, the number of factors of $$3^np^2$$ is $$(4+1)(2+1) = 15.$$ Since we have a unique solution, both conditions together are sufficient. Therefore, C is the answer. 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 &nbs [#permalink] 26 Jul 2018, 23:49
Display posts from previous: Sort by