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# PS OG 424

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Manager
Joined: 05 Oct 2005
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25 Nov 2005, 12:23
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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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SVP
Joined: 28 May 2005
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25 Nov 2005, 12:36
it should be B.

first of all n<100 and 14n/60 is an integer.

that means 7/30 * n = an integer
that means n will be 30, 60, 90, 120, 150, 180

each of these has only 3 different prime factor 2,3 and 5

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hey ya......

VP
Joined: 06 Jun 2004
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25 Nov 2005, 12:36

Rewrite the equation as 14n/60 ==> 7n/30 ==> 7*(n/30)

n must be a multiple of 30. Let n = 30

30's factors are 1, 2, 3, 5 ==> Only 2, 3, 5 are prime.
Re: PS OG 424   [#permalink] 25 Nov 2005, 12:36
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