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

 It is currently 14 Dec 2018, 12:15

### 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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Typical Day of a UCLA MBA Student - Recording of Webinar with UCLA Adcom and Student

December 14, 2018

December 14, 2018

10:00 PM PST

11:00 PM PST

Carolyn and Brett - nicely explained what is the typical day of a UCLA student. I am posting below recording of the webinar for those who could't attend this session.
• ### Free GMAT Strategy Webinar

December 15, 2018

December 15, 2018

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# How many different prime factors does positive integer n have?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51215
How many different prime factors does positive integer n have?  [#permalink]

### Show Tags

14 May 2015, 04:25
2
16
00:00

Difficulty:

95% (hard)

Question Stats:

43% (02:07) correct 57% (02:08) wrong based on 399 sessions

### HideShow timer Statistics

How many different prime factors does positive integer n have?

(1) 44 < n^2 < 99
(2) 8n^2 has twelve factors

Kudos for a correct solution.

_________________
Current Student
Joined: 13 May 2011
Posts: 178
Concentration: Strategy, Technology
GMAT 1: 750 Q49 V42
GPA: 3.2
WE: Accounting (Consulting)
How many different prime factors does positive integer n have?  [#permalink]

### Show Tags

14 May 2015, 08:33
4
2
1) only three positive integers can be derived: 7, 8, 9. Each has only one distinct prime (7, 2 and 3 respectively). Sufficient

2) to calculate number of factors we need to find prime factorization of a number, add 1 to the powers and multiply those powers, 8 breaks to $$2^3$$, hence it has four factors (power of 3 + 1): 1, 2, 4, 8

We need another 2 primes to get twelve factors ($$2^3 * x^2$$ => ($$3+1)*(2+1) = 12$$), square root will double the primes, so we know that n has only one prime. Sufficient

_________________

Stay positive! ^.^

My blog - http://www.mbafortech.com

Retired Moderator
Joined: 29 Apr 2015
Posts: 843
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
How many different prime factors does positive integer n have?  [#permalink]

### Show Tags

Updated on: 14 May 2015, 23:37
Bunuel wrote:
How many different prime factors does positive integer n have?

(1) 44 < n^2 < 99
(2) 8n^2 has twelve factors

Kudos for a correct solution.

Let me try to explain:

If n is a positive integer:

(1) 44 < n^2 < 99
This means, n can be 7, 8 or 9 > all numbers with each 1 distinct prime factor 7(7). 8(2) and 9(3). Therefore Stat. 1 Sufficient

(2) 8n^2 has twelve factors
8^n2 has twelve factors. 8 on its own has 4 factors (1, 2, 4, 8), i.e. we need 8 more factors. N could be any number providing 4 factors. If n = 7, n could have 2 and 7 as prime factors which are 2 distinct factors. Therefore Stat. 2 IS.

Therefore, after reviewing, I suppose it's A Thanks for your inputs EMPOWERgmatRichC
_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

Originally posted by reto on 14 May 2015, 05:44.
Last edited by reto on 14 May 2015, 23:37, edited 3 times in total.
##### General Discussion
Senior Manager
Joined: 21 Jan 2015
Posts: 355
Location: India
Concentration: Strategy, Marketing
GMAT 1: 620 Q48 V28
GMAT 2: 690 Q49 V35
WE: Sales (Consumer Products)
How many different prime factors does positive integer n have?  [#permalink]

### Show Tags

Updated on: 15 May 2015, 02:05
1
Bunuel wrote:
How many different prime factors does positive integer n have?

(1) 44 < n^2 < 99
(2) 8n^2 has twelve factors

Ans: D

Solution: Different prime factors of integer n? we do not know the exact value of n so finding specific value is necessery and then we can find the number of factors.
1) it gives us three values of n=7,8,9 their square[49,64,81] satisfy the range
Now question asks us how many prime factors does n have
if N=7; number of prime factors =1
if N=8; number of prime factors = 1
if N=9; number of prime factors = 1
respectively. [sufficient]

2) 8n^2 has tweleve factors
to make is easier we write it like this (2^3)*(n^2)
now the total number of factors for this is = 4*x=12; x=3: means n needs to be a prime number.
so it can have any prime value. again we know as n being the prime number it has only one prime factor. [Sufficient]

Thank You for the hint, previously i solved it for total number of factors.
Hope this is correct this time.
Ans: D
_________________

--------------------------------------------------------------------
The Mind is Everything, What we Think we Become.

Originally posted by D3N0 on 14 May 2015, 19:52.
Last edited by D3N0 on 15 May 2015, 02:05, edited 1 time in total.
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13081
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: How many different prime factors does positive integer n have?  [#permalink]

### Show Tags

14 May 2015, 21:12
Hi All,

You have to be VERY careful with this prompt; pay attention to the details, write EVERYTHING down and answer the question that is ASKED. Notice that the question asks how many DIFFERENT PRIME FACTORS N has....

It's a pretty safe bet that you all determined that, in Fact 1, N could be 7, 8 or 9.

How many DIFFERENT PRIME FACTORS does 7 have?
How many DIFFERENT PRIME FACTORS does 8 have?
How many DIFFERENT PRIME FACTORS does 9 have?

So what does this tell you about Fact 1?

Knowing that you have to be more detail-oriented with your work, how will you now handle Fact 2?

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** Intern Joined: 16 Jun 2010 Posts: 19 How many different prime factors does positive integer n have? [#permalink] ### Show Tags 15 May 2015, 01:40 3 How many different prime factors does positive integer n have? (1) 44 < n^2 < 99 (2) 8n^2 has twelve factors Solution: (1) 44 < n^2 < 99 --> n could be 7, 8 or 9. - 7: 1 prime factor which is 7 - 8: 1 prime factor which is 2 - 9: 1 prime factor which is 3 --> (1) is sufficient (2)8n^2 has twelve factors: 8n^2 can be re-written as (2^3)*(n^2) Number of factors of (2^3)*(n^2) is 12, or (3+1)*(x+1) = 12, x is the number of factor of n^2 --> n^2 has 2 factors which are n and n^2 --> n is prime number --> n has 1 prime factor --> (2) is sufficient. D is the answer. Current Student Joined: 13 May 2011 Posts: 178 Concentration: Strategy, Technology GMAT 1: 750 Q49 V42 GPA: 3.2 WE: Accounting (Consulting) Re: How many different prime factors does positive integer n have? [#permalink] ### Show Tags 15 May 2015, 08:10 reto wrote: Bunuel wrote: How many different prime factors does positive integer n have? (1) 44 < n^2 < 99 (2) 8n^2 has twelve factors Kudos for a correct solution. Let me try to explain: If n is a positive integer: (1) 44 < n^2 < 99 This means, n can be 7, 8 or 9 > all numbers with each 1 distinct prime factor 7(7). 8(2) and 9(3). Therefore Stat. 1 Sufficient (2) 8n^2 has twelve factors 8^n2 has twelve factors. 8 on its own has 4 factors (1, 2, 4, 8), i.e. we need 8 more factors. N could be any number providing 4 factors. If n = 7, n could have 2 and 7 as prime factors which are 2 distinct factors. Therefore Stat. 2 IS. Therefore, after reviewing, I suppose it's A Thanks for your inputs EMPOWERgmatRichC Prime factor can't have two prime factors within itself. Factors of 7 are "7" and "1". To check, let's put 7 in the formula from second statement: 8 * 7^2 = 2 * 2 * 2 * 7 * 7 = 2^3 * 7^2, > (3+1) * (2+1) = 12. But you get only "sevens" from 7. 2's come from 8, and question asks only about n. _________________ Stay positive! ^.^ My blog - http://www.mbafortech.com Manager Status: Kitchener Joined: 03 Oct 2013 Posts: 89 Location: Canada Concentration: Finance, Finance GPA: 2.9 WE: Education (Education) Re: How many different prime factors does positive integer n have? [#permalink] ### Show Tags 16 May 2015, 08:55 the answer is A statment 1 suff / N^2 could be 49,64,81 and all of these numbers have one prime number statment 2 insuff/ if n is prime number then n has one prime number but if not then n could has more than one prime number for example if n=3 then 8n^2=2^3*3^2 the nimber of factors is 12 and n is prime however if x=6 in this case also the number of factors will be = 12 but x has two prime factors 2,3 _________________ Click +1 Kudos if my post helped Current Student Joined: 13 May 2011 Posts: 178 Concentration: Strategy, Technology GMAT 1: 750 Q49 V42 GPA: 3.2 WE: Accounting (Consulting) Re: How many different prime factors does positive integer n have? [#permalink] ### Show Tags 16 May 2015, 10:41 23a2012 wrote: the answer is A statment 1 suff / N^2 could be 49,64,81 and all of these numbers have one prime number statment 2 insuff/ if n is prime number then n has one prime number but if not then n could has more than one prime number for example if n=3 then 8n^2=2^3*3^2 the nimber of factors is 12 and n is prime however if x=6 in this case also the number of factors will be = 12 but x has two prime factors 2,3 Could you clarify why x=6 gives you 12 factors? If n=6, then 8 * 6^2 = 2 * 2 * 2 * 3*2 * 3*2 = 2^5 * 3^2, hence (5+1) * (2+1) = 18 factors. _________________ Stay positive! ^.^ My blog - http://www.mbafortech.com Math Expert Joined: 02 Sep 2009 Posts: 51215 Re: How many different prime factors does positive integer n have? [#permalink] ### Show Tags 18 May 2015, 07:47 Bunuel wrote: How many different prime factors does positive integer n have? (1) 44 < n^2 < 99 (2) 8n^2 has twelve factors Kudos for a correct solution. OFFICIAL SOLUTION: How many different prime factors does positive integer n have? (1) 44 < n^2 < 99. This implies that n can be 7, 8, or 9. Each of these numbers have 1 prime: 7, 2, and 3, respectively. Sufficient. (2) 8n^2 has twelve factors. For $$8n^2=2^3n^2$$ to have twelve factors n must be a prime: $$2^3*(prime)^2$$ --> number of factors = (3+1)(2+1)=12. Sufficient. Answer: D. _________________ VP Joined: 05 Mar 2015 Posts: 1004 Re: How many different prime factors does positive integer n have? [#permalink] ### Show Tags 14 Oct 2015, 23:45 Bunuel wrote: Bunuel wrote: How many different prime factors does positive integer n have? (1) 44 < n^2 < 99 (2) 8n^2 has twelve factors Kudos for a correct solution. OFFICIAL SOLUTION: How many different prime factors does positive integer n have? (1) 44 < n^2 < 99. This implies that n can be 7, 8, or 9. Each of these numbers have 1 prime: 7, 2, and 3, respectively. Sufficient. (2) 8n^2 has twelve factors. For $$8n^2=2^3n^2$$ to have twelve factors n must be a prime: $$2^3*(prime)^2$$ --> number of factors = (3+1)(2+1)=12. Sufficient. Answer: D. Hello bunuel Plz clear me if my approach is wrong... As per (1) 44<n^2<99 or 4<n^2/11<9 for n to be +ve integer it should be either 5 or 7(2 primes) so, sufficient. Retired Moderator Joined: 29 Apr 2015 Posts: 843 Location: Switzerland Concentration: Economics, Finance Schools: LBS MIF '19 WE: Asset Management (Investment Banking) Re: How many different prime factors does positive integer n have? [#permalink] ### Show Tags 15 Oct 2015, 02:38 rohit8865 wrote: Bunuel wrote: Bunuel wrote: How many different prime factors does positive integer n have? (1) 44 < n^2 < 99 (2) 8n^2 has twelve factors Kudos for a correct solution. OFFICIAL SOLUTION: How many different prime factors does positive integer n have? (1) 44 < n^2 < 99. This implies that n can be 7, 8, or 9. Each of these numbers have 1 prime: 7, 2, and 3, respectively. Sufficient. (2) 8n^2 has twelve factors. For $$8n^2=2^3n^2$$ to have twelve factors n must be a prime: $$2^3*(prime)^2$$ --> number of factors = (3+1)(2+1)=12. Sufficient. Answer: D. Hello bunuel Plz clear me if my approach is wrong... As per (1) 44<n^2<99 or 4<n^2/11<9 for n to be +ve integer it should be either 5 or 7(2 primes) so, sufficient. I am not Bunuel, but I can help. Cou have to read the question stem carefully. What is it asking? "How many different prime factors does positive integer n have?" You can answer this right away with the fact that n can either be 5 or 7 because both of these numbers have just one prime factor right? Does it help? _________________ Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS! PS Please send me PM if I do not respond to your question within 24 hours. Intern Joined: 17 May 2015 Posts: 1 Re: How many different prime factors does positive integer n have? [#permalink] ### Show Tags 19 Oct 2015, 12:40 How many different prime factors does positive integer n have? (1) 44 < n^2 < 99 (2) 8n^2 has twelve factors I have doubt about (2). What if n is 16? then 2^3*2^8=2^11 and it has 11+1=12 factors but it has only one prime factor, which is 2. Can anyone tell me what I am missing? Retired Moderator Joined: 29 Apr 2015 Posts: 843 Location: Switzerland Concentration: Economics, Finance Schools: LBS MIF '19 WE: Asset Management (Investment Banking) How many different prime factors does positive integer n have? [#permalink] ### Show Tags 20 Oct 2015, 02:16 1 Yiva wrote: How many different prime factors does positive integer n have? (1) 44 < n^2 < 99 (2) 8n^2 has twelve factors I have doubt about (2). What if n is 16? then 2^3*2^8=2^11 and it has 11+1=12 factors but it has only one prime factor, which is 2. Can anyone tell me what I am missing? Statement 2 tells you that n must be prime because 8 = 2^3 which gives you (3+1) factors and for 8n^2 to have exactly 12 factors, n must be prime in order to have (3+1)(2+1). If n is prime, it has how many different PRIME Factors Yiva? Yes exactly, if n is prime, n will have exactly 1 prime factor. The question can be answered. _________________ Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS! PS Please send me PM if I do not respond to your question within 24 hours. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6639 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: How many different prime factors does positive integer n have? [#permalink] ### Show Tags 22 Oct 2015, 12:39 2 Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. How many different prime factors does positive integer n have? (1) 44 < n^2 < 99 (2) 8n^2 has twelve factors The question has one variable (n) and 2 equations are given, so there is high chance (D) will be our answer. From condition 1, n^2=49,64,81, and n=7,8,9=7,2^3,3^2. There is only 1 case where there are different prime factors, so this is sufficient. For condition 2, 8n^2=2^3n^2==>(3+1)(2+1)=12. n has to be prime. This also gives that there is only 1 case where there are different prime factors, so this is also sufficient. The answer becomes (D). For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or 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. "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"

Retired Moderator
Joined: 29 Apr 2015
Posts: 843
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
Re: How many different prime factors does positive integer n have?  [#permalink]

### Show Tags

22 Oct 2015, 12:42
MathRevolution wrote:
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

How many different prime factors does positive integer n have?

(1) 44 < n^2 < 99
(2) 8n^2 has twelve factors

The question has one variable (n) and 2 equations are given, so there is high chance (D) will be our answer.
From condition 1, n^2=49,64,81, and n=7,8,9=7,2^3,3^2. There is only 1 case where there are different prime factors, so this is sufficient.
For condition 2, 8n^2=2^3n^2==>(3+1)(2+1)=12. n has to be prime. This also gives that there is only 1 case where there are different prime factors, so this is also sufficient.

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

Current Student
Joined: 12 Aug 2015
Posts: 2627
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: How many different prime factors does positive integer n have?  [#permalink]

### Show Tags

10 Jan 2017, 01:04
Excellent Question.
Here is my solution to this one =>

We need the number of prime factors for n.

Statement 1->
Notice the boundary condition for n is given.
Since n is an integer => n^2 must be a perfect square.
n^2=> 49,64 or 81
So n can be 7 or 2^3 or 3^2
In each case -> n will have just one prime factor.
Hence Sufficient.

Statement 2->
8n^12 has twelve factors.
2^3*n^2 has 12 factors => This is only possible if n is a prime number.
Thus it will have only one prime factor.
Hence D.

_________________

MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

Manager
Joined: 28 Jul 2016
Posts: 134
Re: How many different prime factors does positive integer n have?  [#permalink]

### Show Tags

06 Apr 2017, 04:58
Great question! thanks for sharing this.
Manager
Joined: 18 Apr 2018
Posts: 74
Re: How many different prime factors does positive integer n have?  [#permalink]

### Show Tags

29 Jun 2018, 04:43
I agree with all the explanations but have a question though... If n can be 7,8 or 9, which isn't a definite value, does that make the answer sufficient?

Posted from my mobile device
Math Expert
Joined: 02 Sep 2009
Posts: 51215
Re: How many different prime factors does positive integer n have?  [#permalink]

### Show Tags

29 Jun 2018, 04:50
Kem12 wrote:
I agree with all the explanations but have a question though... If n can be 7,8 or 9, which isn't a definite value, does that make the answer sufficient?

Posted from my mobile device

The question does not ask "what is the value of n", it asks "How many different prime factors does positive integer n have". So, for (1), even though n can take three values, each of those values still has only one prime factor. For (2) we get that n is a prime number, so it must have only one prime factor. Thus, both statements give that n has ONE prime factor.
_________________
Re: How many different prime factors does positive integer n have? &nbs [#permalink] 29 Jun 2018, 04:50

Go to page    1   2    Next  [ 21 posts ]

Display posts from previous: Sort by