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# The positive integer x has how many different positive

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The positive integer x has how many different positive [#permalink]

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12 Aug 2006, 16:57
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The positive integer x has how many different
positive factors?
(1) x is a multiple of the same number of
positive integers that 75 is.
(2) x = a2b where a and b are prime numbers.
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12 Aug 2006, 18:07
I believe it's A.
75 factors = 5,5,3.

a2b can mean two things.
a=3, b=5 which gives 3 factors.
or
a=3,b=2 which gives 2 factors.
So, B is insufficient.
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13 Aug 2006, 10:12
I think the answer here is B

ST 1 Same number of factors

75 has a total of 6 factors so x would also have the same number of factors (i.e. 6) and plus k more (x is a multiple of those factors)

ST 2 I am assuming is a^2b => Total number of factors will be 3*2 = 6 hence SUFF
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13 Aug 2006, 11:37
I agree with gmatornot in answer choice B.

ST1: If you mean factors, there are 5 (1,3,5,25,75). If you mean numbers multiplied to make 75, that is unclear, bc it could be 1x75 or 3x5x5, so that would be 2 or 3 numbers. In any event, you can make a heck of a lot of different numbers when you multiply 5 numbers together, or 2 numbers together, or 3 numbers together. Each might have a different number of factors.

ST2: Although it needs some clarification in whether it is supposed to be a^2b or (a^2)(b), ST2 will give you a definitive number of factors.

[quote="gmatornot"]I think the answer here is B

ST 1 Same number of factors

75 has a total of 6 factors so x would also have the same number of factors (i.e. 6) and plus k more (x is a multiple of those factors)

ST 2 I am assuming is a^2b => Total number of factors will be 3*2 = 6 hence SUFF[/quote]
13 Aug 2006, 11:37
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# The positive integer x has how many different positive

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