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# PS OG 424

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Manager
Joined: 05 Oct 2005
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PS OG 424 [#permalink]  25 Nov 2005, 11:24
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Hi
can anyone explain me how to approach this one ?
Thanks
IF n is a positive integer less than 2OO and 14n/6O is an integer then n has how many different positive prime factors?

A 2
B 3
C 5
D 6
E 8
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Director
Joined: 27 Jun 2005
Posts: 515
Location: MS
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B

tough one ....trying to make better guess

maximum value of n can be

7*n/30 = Integer n can be at maximum 180

which has prime factors as 2 3 5 ....
Manager
Joined: 15 Aug 2005
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Re: PS OG 424 [#permalink]  25 Nov 2005, 13:55
mand-y wrote:
:) Hi
can anyone explain me how to approach this one ?
Thanks
IF n is a positive integer less than 2OO and 14n/6O is an integer then n has how many different positive prime factors?

A 2
B 3
C 5
D 6
E 8

I would go with B too.

14n/60 is an integer or 7n/30 is an integer.
so n must be a multiple of 30 (positive prime factors of 30 are 2,3, & 5) and we know n < 200.
=> n = 30X where x can be 1,2,3,4,5,6 (X cannot be > 6 otherwise n > 200)
=> so the prime factors of n are the same as the Possible prime factors of 30 - 2,3,5
Manager
Joined: 05 Oct 2005
Posts: 200
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oa is B
THANKS
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