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

 It is currently 09 Dec 2019, 12:21 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Positive integer N has exactly 12 unique factors. What is the largest

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 59623
Positive integer N has exactly 12 unique factors. What is the largest  [#permalink]

### Show Tags

1
11 00:00

Difficulty:   45% (medium)

Question Stats: 61% (01:18) correct 39% (01:23) wrong based on 274 sessions

### HideShow timer Statistics

Positive integer N has exactly 12 unique factors. What is the largest possible number of unique prime factors that N could have?

(A) 2
(B) 3
(C) 7
(D) 11
(E) 12 This question was provided by Veritas Prep for the Game of Timers Competition _________________
Manager  B
Joined: 17 Jan 2014
Posts: 54
Location: India
Concentration: Operations, Marketing
WE: Supply Chain Management (Manufacturing)
Re: Positive integer N has exactly 12 unique factors. What is the largest  [#permalink]

### Show Tags

because 12 unique factors ...in answer choice, 11 is the larger prime number.
Manager  G
Joined: 08 Jan 2018
Posts: 129
Positive integer N has exactly 12 unique factors. What is the largest  [#permalink]

### Show Tags

2
Positive integer N can have exactly 12 unique factors in any of the following ways:

12*1 -> (11 + 1) -> $$A^11$$ -> 1 prime factor
6*2 -> (5+1)(1+1) -> $$A^5*B^1$$ -> 2 prime factors
4*3 -> (3+1)(2+1) -> $$A^3*B^2$$ -> 2 prime factors
2*2*3 -> (1+1)(1+1)(2+1) ->$$A^1*B^1*C^2$$ -> 3 prime factorsThis one being the largest.

Originally posted by Sayon on 18 Jul 2019, 08:14.
Last edited by Sayon on 18 Jul 2019, 23:06, edited 1 time in total.
Director  P
Joined: 16 Jan 2019
Posts: 507
Location: India
Concentration: General Management
WE: Sales (Other)
Re: Positive integer N has exactly 12 unique factors. What is the largest  [#permalink]

### Show Tags

1
$$12=2*2*3$$

So $$N=p1^a*p2^b*p3^c$$ where $$p1, p2 and p3$$ are distinct prime number and one of $$a, b and c$$ can be 2 while the other two are 1

This is because if $$N$$ had 4 unique prime factors, $$N=p1^1*p2^1*p3^1*p4^1$$ the number of factors becomes 16

So N can have a maximum of 3 unique prime factors

Manager  G
Joined: 26 Jan 2016
Posts: 181
Re: Positive integer N has exactly 12 unique factors. What is the largest  [#permalink]

### Show Tags

12 unique factors means 11 prime factors + 1 as factor.
therefore 11 unique prime factors.

Hence D
ISB School Moderator G
Joined: 08 Dec 2013
Posts: 616
Location: India
Concentration: Nonprofit, Sustainability
Schools: ISB '21
GMAT 1: 630 Q47 V30 WE: Operations (Non-Profit and Government)
Re: Positive integer N has exactly 12 unique factors. What is the largest  [#permalink]

### Show Tags

1
Total unique factors => 12= (2)*(2)*(3)...To maximize the count of prime factors
12= (1+1) * (1+1)* (2+1), so there can be three distinct prime numbers that are also factors of N.
SVP  D
Joined: 03 Jun 2019
Posts: 1880
Location: India
Positive integer N has exactly 12 unique factors. What is the largest  [#permalink]

### Show Tags

1
Positive integer N has exactly 12 unique factors. What is the largest possible number of unique prime factors that N could have?

(A) 2
(B) 3
(C) 7
(D) 11
(E) 12

No of unique factors of positive integer N = 12
12 = 2*2*3 = 4*3 = 2*6 = 12
Therefore

$$N = P_1*P_2*P_3^2$$ for 12 = 2*2*3. No of unique prime factors = 3 (1)
or
$$N = P_1^3*P_2^2$$ for 12 = 4*3 No of unique prime factors = 2 (2)
or
$$N= P_1*P_2^5$$ for 12 = 2*6 No of unique prime factors = 2 (3)
or
$$N= P_1^11$$ for 12 = 12 No of unique prime factors = 1 (4)

We see that for equation (1), no of unique prime factors = 3 is largest possible number of unique prime factors

IMO B
Manager  S
Joined: 27 Mar 2018
Posts: 79
Location: India
Re: Positive integer N has exactly 12 unique factors. What is the largest  [#permalink]

### Show Tags

3
N has 12 factors so it isn't a perfect square.

Total number of factors of N= a^m * b^n *... is calculated as-
(m+1)*(n+1)*..
To get 12 as total factors, largest possible number of unique prime factors is 3-
a^1*b^1*c^2

=> (1+1)*(1+1)*(2+1) = 12

Hence option B
Intern  B
Joined: 26 May 2018
Posts: 45
Re: Positive integer N has exactly 12 unique factors. What is the largest  [#permalink]

### Show Tags

Positive integer N has exactly 12 unique factors. What is the largest possible number of unique prime factors that N could have?

(A) 2

12=2ˆ2*3; so 2 unique factors
Senior Manager  P
Joined: 27 Aug 2014
Posts: 368
Location: Netherlands
Concentration: Finance, Strategy
Schools: LBS '22, ISB '21
GPA: 3.9
WE: Analyst (Energy and Utilities)
Re: Positive integer N has exactly 12 unique factors. What is the largest  [#permalink]

### Show Tags

1

N = a1^x*a2^y*a3^z....
number of factors = (x+1)*(y+1)*(z+1)...
as number of factors are 12 = 2*2*3
we can represent N as a1*a2*a3^2, where a1,a2 and a3 are primes, so 3 primes

Director  P
Joined: 04 Sep 2015
Posts: 665
Location: India
WE: Information Technology (Computer Software)
Re: Positive integer N has exactly 12 unique factors. What is the largest  [#permalink]

### Show Tags

1
IMO : B

Positive integer N has exactly 12 unique factors. What is the largest possible number of unique prime factors that N could have?

(A) 2
(B) 3
(C) 7
(D) 11
(E) 12

SOL:

if there are 12 unique factors then we know that the number of factors= (power of unique prime +1)(power of other unique prime +1)(.... so on)

so we know that 12 has following factors

2*6 (1 prime has power 1 and other prime has power 5)
2*2*3(2 primes have power 1 and 1 prime has power 2)

only the above combination is possible.

so we can safely say that 3 is the correct answer.

why not 7 ,11 or 12... heres why,if there are 12 unique primes then all of them has to have power 0 and then all the values will be=1.
similarly for 11 because it will still make atleast 1 prime to have power as 0 then it will be 1 and 1 is not a prime. similarly for 7 atleast one of the prime factors has to have power 0 so it will also not make a prime factor.
Senior Manager  G
Joined: 05 Mar 2017
Posts: 260
Location: India
Concentration: General Management, Marketing
GPA: 3.6
WE: Marketing (Hospitality and Tourism)
Re: Positive integer N has exactly 12 unique factors. What is the largest  [#permalink]

### Show Tags

1
Positive integer N has exactly 12 unique factors. What is the largest possible number of unique prime factors that N could have?

(A) 2
(B) 3
(C) 7
(D) 11
(E) 12

This question is from the number of properties.
We know that the total number of factors is the multiplication of powers +1 of the prime numbers.
12 = 2*2*3
Which means that it will have 3 uniques factors.

Manager  S
Joined: 17 Apr 2018
Posts: 107
Re: Positive integer N has exactly 12 unique factors. What is the largest  [#permalink]

### Show Tags

1
Let number N=a^p.b^q.....

Number of factors would be (p+1)(q+1)....

let's break 12 into maximum no of factors greater than 1

12 = 2X2X3
so N= a^2.b^2.c^3

Hence, Maximum no of unique prime factors = 3

Manager  P
Joined: 13 May 2017
Posts: 121
Location: Finland
Concentration: Accounting, Entrepreneurship
GMAT 1: 530 Q42 V22 GMAT 2: 570 Q36 V31 GMAT 3: 600 Q42 V28 GPA: 3.14
WE: Account Management (Entertainment and Sports)
Re: Positive integer N has exactly 12 unique factors. What is the largest  [#permalink]

### Show Tags

1
N = p1^a*p2^b*p3^c , in which p1,p2, and p3 are different primes and a,b, and c are the exponents of those different primes
Number of factors of N= (a+1)(b+1)(c+1)=12
12 could be the multiple of 2*6, 3*4, or 3*2*2, each of these represents the exponent+1 of one prime; so with more exponents we can maximize the number of primes within N.

The max number of prime we can have is 3.

Please note that 1*2*2*3 doesn't work. This would mean p1^0*p2^1... so p1 is not factor of N
Manager  G
Joined: 30 May 2018
Posts: 157
GMAT 1: 710 Q49 V36 GPA: 3.8
Re: Positive integer N has exactly 12 unique factors. What is the largest  [#permalink]

### Show Tags

1
B

This looks like a very straight forward question unless I am missing something which I feel I am. Hopefully I am wrong.

N has 12 unique factors, which means no of factors of N is 12. Note that factors of 12 are 2*2*3. So, N could be, N = 2^3*3^2 or N = 2*3*5^2. The no of prime factors in these two cases are 2 and 3, respectively.

So maximum possible factors are 3.
Manager  G
Joined: 10 Mar 2019
Posts: 75
Location: Russian Federation
Schools: Booth, Berkeley Haas
GMAT 1: 730 Q50 V39 GPA: 3.95
Re: Positive integer N has exactly 12 unique factors. What is the largest  [#permalink]

### Show Tags

1
Positive integer N has exactly 12 unique factors. What is the largest possible number of unique prime factors that N could have

Factorization formula is a power of the prime number +1 and then multiply them.
We should have as many prime numbers as we can, so 2*2*3
3 is the largest possible number of prime numbers

IMO B
Manager  S
Joined: 11 Feb 2018
Posts: 80
Re: Positive integer N has exactly 12 unique factors. What is the largest  [#permalink]

### Show Tags

If N>0 and has 12 unique factors, then the maximum number of prime factors N can have is also 12. Consider: $$N= 2*3*5*7*11*13*17*19*23*29*31*37$$, N here has 12 unique factors all of which are prime.

Senior Manager  P
Joined: 10 Jan 2017
Posts: 330
Location: India
Re: Positive integer N has exactly 12 unique factors. What is the largest  [#permalink]

### Show Tags

1
IMO correct answer is B - 3; explanation is provided as attachment
Attachments IMG_20190718_211608.JPG [ 949.98 KiB | Viewed 1738 times ]

BSchool Moderator G
Joined: 07 Dec 2018
Posts: 146
Location: India
Re: Positive integer N has exactly 12 unique factors. What is the largest  [#permalink]

### Show Tags

1
Positive integer N has exactly 12 unique factors. What is the largest possible number of unique prime factors that N could have?

(A) 2
(B) 3
(C) 7
(D) 11
(E) 12

N has exactly 12 unique factors

12 can be written as
12*1
6*2
3*4
2*2*3

No. of unique factors = sum of the power of prime factors+1

So, to maximize the number of unique factors we should choose 2*2*3 option.
N=p1*p2*$$p3^2$$

Hence we get 3 prime factors.

If we could have split the number into 4, we would have chosen that option.

Hence, Ans should be (B)
Director  P
Joined: 24 Nov 2016
Posts: 935
Location: United States
Re: Positive integer N has exactly 12 unique factors. What is the largest  [#permalink]

### Show Tags

1
Quote:
Positive integer N has exactly 12 unique factors. What is the largest possible number of unique prime factors that N could have?

(A) 2
(B) 3
(C) 7
(D) 11
(E) 12

num.factors of an integer x is the product of the powers of the "prime factors of x + 1"
test some cases num.f(N)=12, we find that the max is 3:
N=2ˆ11=(11+1)=12 <= 1 prime
N=2ˆ3*3ˆ2=(3+1)(3)=12 <= 2 primes
N=2ˆ2*3*5=(2+1)(2)(2)=12 <= 3 primes
N=2*3*5*7=(2)(2)(2)(2)=16 cant be. Re: Positive integer N has exactly 12 unique factors. What is the largest   [#permalink] 18 Jul 2019, 08:52

Go to page    1   2   3   4   5    Next  [ 84 posts ]

Display posts from previous: Sort by

# Positive integer N has exactly 12 unique factors. What is the largest  