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If x a positive integer and has twelve positive factors, what is the s
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25 Jun 2021, 08:49
25 Jun 2021, 08:49
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If x a positive integer and has twelve positive factors, what is the smallest possible value of x?
A. 2048
B. 486
C. 96
D. 72
E. 60
A. 2048
B. 486
C. 96
D. 72
E. 60
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Re: If x a positive integer and has twelve positive factors, what is the s
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25 Jun 2021, 08:55
25 Jun 2021, 08:55
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Carcass wrote:
If x a positive integer and has twelve positive factors, what is the smallest possible value of x?
A. 2048
B. 486
C. 96
D. 72
E. 60
A. 2048
B. 486
C. 96
D. 72
E. 60
If you're not sure how to start with this question, don't waste a ton of time searching for a solution.
Instead, use the answer choices to your advantage.
We'll start with the smallest value and work our way up (since we're looking for the smallest possible value of x)
----------------------------
To determine the number of divisors of each answer choice, we'll use this handy trick:
If the prime factorization of N = (p^a)(q^b)(r^c) . . . (where p, q, r, etc are different prime numbers), then N has a total of (a+1)(b+1)(c+1)(etc) positive divisors.
Example: 14000 = (2^4)(5^3)(7^1)
So, the number of positive divisors of 14000 = (4+1)(3+1)(1+1) =(5)(4)(2) = 40
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E. 60
60 = (2)(2)(3)(5) = (2^2)(3^1)(5^1)
So, the number of positive divisors of 60 = (2+1)(1+1)(1+1) =(3)(2)(2) = 12
Voila!!
Answer: E
Cheers,
Brent
gmatclubot
Re: If x a positive integer and has twelve positive factors, what is the s [#permalink]
25 Jun 2021, 08:55
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