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different factors

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different factors

by gmat740 » Sat Aug 08, 2009 9:21 pm
How many different factors does the integer n have?
(1) n = (a^4)*(b^3), where a and b are different positive prime numbers.
(2) The only positive prime numbers that are factors of n are 5 and 7.
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Source: — Data Sufficiency |
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by gmatismybane » Sun Aug 09, 2009 12:19 am
I think the answer is A.

1) Sufficient because factors are:

1 and (a^4)(b^3)
a and (a^3)(b^3)
a^2 and (a^2)(b^3)
a^3 and (a)(b^3)
a^4 and b^3
so on so forth... clearly you can get a distinct countable value for the number of factors.

2) Insufficient because it only states 5 and 7 are prime factors... so:

if n = 35 then the answer to the question is 4 (1, 5, 7, 35)
if n = 165 then the answer to the question is 6 (1, 5, 7, 25, 35, 165)

so therefore insufficient.
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by anand0408 » Sun Aug 09, 2009 2:19 am
yup agree. A
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