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

 It is currently 24 Aug 2019, 00:32

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

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

Author Message
TAGS:

Hide Tags

Manager
Joined: 12 Mar 2019
Posts: 111
Re: Positive integer N has exactly 12 unique factors. What is the largest  [#permalink]

Show Tags

19 Jul 2019, 23:30
Kinshook wrote:
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

Hello ,
I have small doubt as i am new to this concept. I understand rule of finding factors : power +1 : But question stem says N has 12 unique factors. In all cases you presented, if P2^2 or P^3 it means, its p2*p2 or p3*p3*p3, How can we take this as question says it has Unique factors, but from this we have 2 times P2 and 3 times P3, which cannot be unique as its repeating. Don't condition itself falls at time of assumption as it doesnot have unique 12 factors, Can't it be p1,p2,p3----p12 .
Hope i am able to explain my question
Manager
Status: Not Applying
Joined: 27 Apr 2009
Posts: 179
Location: India
Schools: HBS '14 (A)
GMAT 1: 730 Q51 V36
Re: Positive integer N has exactly 12 unique factors. What is the largest  [#permalink]

Show Tags

19 Jul 2019, 23:42
rishab0507 wrote:
Kinshook wrote:
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

Hello ,
I have small doubt as i am new to this concept. I understand rule of finding factors : power +1 : But question stem says N has 12 unique factors. In all cases you presented, if P2^2 or P^3 it means, its p2*p2 or p3*p3*p3, How can we take this as question says it has Unique factors, but from this we have 2 times P2 and 3 times P3, which cannot be unique as its repeating. Don't condition itself falls at time of assumption as it doesnot have unique 12 factors, Can't it be p1,p2,p3----p12 .
Hope i am able to explain my question

When we say N = a^p * b^q, then we mean that N has (p + 1) * (q + 1) unique factors.

For example 72 = 2^3 * 3^2
Hence, 72 has (3 + 1) * (2 + 1) = 12 unique factors.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
As you can see, there are 12 unique factors and nothing is repeated.

Hope this helps.
_________________
http://www.wizius.in
Better Prep. Better Scores. Better Schools

Guaranteed Admission to Top-50 MBA Programs
You either get-in or get your money-back.
Senior Manager
Joined: 13 Feb 2018
Posts: 448
GMAT 1: 640 Q48 V28
Re: Positive integer N has exactly 12 unique factors. What is the largest  [#permalink]

Show Tags

19 Jul 2019, 23:56
rishab0507

the stem says "unique factors" not "uniques prime factors"

You Assert: " its p2*p2 or p3*p3*p3, How can we take this as question says it has Unique factors, but from this we have 2 times P2 and 3 times P3,"
1) you have to brush basic concepts: $$p^2=2*p$$ is wrong
2) consider p=2, $$p^3=2*2*2=2^3=8$$ You assert that 2*2*2 "cannot be unique as its repeating";
2^3=8 has 4 unique factors, even 2 is repeating: 1, 2, 4, 8

In your example: "p1,p2,p3----p12" this expression has 12 "unique prime factors" and $$2^12$$ "unique factors"

Hope I understood your question well
Intern
Joined: 14 Oct 2018
Posts: 16
Re: Positive integer N has exactly 12 unique factors. What is the largest  [#permalink]

Show Tags

22 Jul 2019, 00:28
Sayon wrote:
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.

I get it how you are coming up with (1+1)(1+1)(2+1) = 12 and hence, 3 prime numbers i.e, 1,1 & 2. But 1 is neither prime nor composite. So, should it not be (3+1)(2+1), 2 prime numbers, 3&2?

Posted from my mobile device
Re: Positive integer N has exactly 12 unique factors. What is the largest   [#permalink] 22 Jul 2019, 00:28

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

Display posts from previous: Sort by