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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]

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2
15 00:00

Difficulty:   95% (hard)

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

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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)

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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

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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 B
Joined: 10 Oct 2012
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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.
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Re: A number has exactly 32 factors out of which 4 are not compo  [#permalink]

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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
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Posts: 13600
Re: A number has exactly 32 factors out of which 4 are not compo  [#permalink]

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_________________ Re: A number has exactly 32 factors out of which 4 are not compo   [#permalink] 14 Sep 2019, 17:33
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