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

 It is currently 18 Nov 2019, 06:47

### 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

# A number has exactly 32 factors out of which 4 are not compo

Author Message
TAGS:

### Hide Tags

Current Student
Joined: 06 Jan 2013
Posts: 25
GPA: 4
WE: Engineering (Transportation)
A number has exactly 32 factors out of which 4 are not compo  [#permalink]

### Show Tags

Updated on: 05 May 2013, 22:54
2
15
00:00

Difficulty:

95% (hard)

Question Stats:

35% (02:11) correct 65% (02:06) wrong based on 99 sessions

### HideShow timer Statistics

A number has exactly 32 factors out of which 4 are not composite. Product of these 4 factors (which are not composite) is 30. How many such numbers are possible?

A. 2
B. 4
C. 6
D. 3
E. Not possible

_________________
If you shut your door to all errors, truth will be shut out.

Originally posted by GMATtracted on 05 May 2013, 11:47.
Last edited by Bunuel on 05 May 2013, 22:54, edited 1 time in total.
RENAMED THE TOPIC.
Intern
Joined: 11 Dec 2012
Posts: 12
Location: India
Concentration: Strategy, Technology
Schools: HKUST '15 (S)
WE: Consulting (Computer Software)

### Show Tags

05 May 2013, 12:05
GMATtracted wrote:
A number has exactly 32 factors out of which 4 are not composite. Product of these 4 factors(which are not composite) is 30. How many such numbers are possible?

A. 2
B. 4
C. 6
D. 3
E. Not possible

The second sentence tells us that the product of 4 prime factors of the original number is 30. The product of 2, 3 and 5 is itself equal to 30, there is no possibility of a fourth factor here. The answer should be E.

Can you please explain why the OA is C.
Intern
Joined: 27 Jul 2012
Posts: 25

### Show Tags

05 May 2013, 13:17
1
4 are not composite factors.
Product of these 4 = 30
if we start with the first prime numbers 2*3*5 that makes it 30.
So the 4 numbers are 1,2,3,5. And all 4 are not composite

Also number of factors for $$2^a$$*$$3^b$$*$$5^c$$ is (a+1)(b+1)(c+1)=32
and a,b,c cannot be 0
so possible combinations of a,b,c are combinations of 7,1,1 (8*2*2=32) and 3,3,2(4*4*2=32)
Each can have 3 combinations.

So this makes it 6 possible numbers
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 584

### Show Tags

05 May 2013, 21:51
1
GMATtracted wrote:
A number has exactly 32 factors out of which 4 are not composite. Product of these 4 factors(which are not composite) is 30. How many such numbers are possible?

A. 2
B. 4
C. 6
D. 3
E. Not possible

Firstly , we should note that 1 is NEITHER a prime nor a composite number.The first composite number is 4.Thus, when the problem states that there are 4 factors that are not composite, these nos are 1,2,3,5. Thus, the given number = 2^a*3^b*5^c. Also, (a+1)*(b+1)*(c+1) = 32. We can break down 32 into 3 integers as : 2*2*8 or 4*4*2
Also, the only possible combinations for a,b,c are : 3,3,1 OR 1,1,7. Thus, each combination has 3 possible orders and we have a total of 6 possibilities.

C.
_________________
Manager
Joined: 14 Sep 2014
Posts: 86
WE: Engineering (Consulting)
Re: A number has exactly 32 factors out of which 4 are not compo  [#permalink]

### Show Tags

13 Dec 2014, 07:24
1
GMATtracted wrote:
A number has exactly 32 factors out of which 4 are not composite. Product of these 4 factors (which are not composite) is 30. How many such numbers are possible?

A. 2
B. 4
C. 6
D. 3
E. Not possible

Let's see data,
i) a number with 32 factors, out of which 4 are not composite (Too vague data)
ii) product of these 4 factors is 30
lets take (ii) data
30 = 2*3*5*1 (1 is natural number i.e not composite nor prime)
so we know 3 factors of number are 2,3,5
now 32 = 2*4*4, 2*2*8
so total numbers possible = 3C1 + 3C1 = 6
Non-Human User
Joined: 09 Sep 2013
Posts: 13600
Re: A number has exactly 32 factors out of which 4 are not compo  [#permalink]

### Show Tags

14 Sep 2019, 17:33
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: A number has exactly 32 factors out of which 4 are not compo   [#permalink] 14 Sep 2019, 17:33
Display posts from previous: Sort by