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How many different factors does the integer n have?

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How many different factors does the integer n have? [#permalink]

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New post 13 Nov 2017, 00:19
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70% (00:34) correct 30% (00:49) wrong based on 46 sessions

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How many different positive factors does the integer n have?

(1) n = (a^4)(b^3) where a and b are different prime numbers.
(2) The only prime numbers that are factors of n are 5 and 7.

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How many different factors does the integer n have? [#permalink]

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New post Updated on: 13 Nov 2017, 01:03
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(1) we know the powers oif prime factors, so using the fornmula we can find total number of different factors= (3+1)*(4+1)= 20 - sufficient
(2) without knowing the powers we cannot figure out total number of factors - insufficient

Answer A

Originally posted by Alexey1989x on 13 Nov 2017, 00:34.
Last edited by Alexey1989x on 13 Nov 2017, 01:03, edited 1 time in total.
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Re: How many different factors does the integer n have? [#permalink]

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New post 13 Nov 2017, 00:57
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Alexey1989x wrote:
(1) n has "a" and "b" as its prime factors, 1 and "n" itself, so the total number is 4 - Sufficient
(2) n has 5;7;1 and 35 itself so in total it has 4 factors - Sufficient

Answer D.


statement B says 3 and 5 are the only prime factors, but it does not mention the powers of each.
Therefore, A should be the answer.
Re: How many different factors does the integer n have?   [#permalink] 13 Nov 2017, 00:57
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