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A number has exactly 32 factors out of which 4 are not compo
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Updated on: 05 May 2013, 22:54
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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
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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.
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Re: GMAT quant(problem solving)
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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.



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Re: GMAT quant(problem solving)
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05 May 2013, 13:17
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



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Re: GMAT quant(problem solving)
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05 May 2013, 21:51
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
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13 Dec 2014, 07:24
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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Re: A number has exactly 32 factors out of which 4 are not compo
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14 Sep 2019, 17:33
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Re: A number has exactly 32 factors out of which 4 are not compo
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