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# If n is 12 times a single-digit non-prime number, what is

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If n is 12 times a single-digit non-prime number, what is [#permalink]

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16 Sep 2006, 06:43
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If n is 12 times a single-digit non-prime number, what is the value of n?

(1) n has more than 10 factors.
(2) More than half of the factors of n are even.

Last edited by kevincan on 16 Sep 2006, 07:16, edited 1 time in total.
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16 Sep 2006, 07:00
Hallo kevin
From A) n can be 12*1, 12*(4^2), 12*(6^2), 12*(8^2), 12*(9^2) so there are more than 1 number with more than 10 factors
n=12*16=3*2^5 has 12 factors
n=12*36=3^3*2^4 has 20 factors
A is NOT sufficient

B) with the examples of 192 and 432 which both have more than half of their factos even seems that B is NOT suff

Taken together we can not determine unique value of n so E) IMO
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16 Sep 2006, 07:17
BG wrote:
Hallo kevin
From A) n can be 12*1, 12*(4^2), 12*(6^2), 12*(8^2), 12*(9^2) so there are more than 1 number with more than 10 factors
n=12*16=3*2^5 has 12 factors
n=12*36=3^3*2^4 has 20 factors
A is NOT sufficient

B) with the examples of 192 and 432 which both have more than half of their factos even seems that B is NOT suff

Taken together we can not determine unique value of n so E) IMO

You're right BG, but I meant to write the question differently. So I've changed it. I hope you don't mind!
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16 Sep 2006, 07:39
I don't mind at all
But think that the ans is the same
A) n can be 12,,48,72,96,108
96=3*(2^5) has 12 factors
108=(2^2)*(3^3) has 12 factors
so A is NOT suff

B) from same examples as above think that B is NOT suff too.

Both together are not suff so E is the ans again
16 Sep 2006, 07:39
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