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200 and 14n/60

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200 and 14n/60

by sanju09 » Wed Apr 08, 2009 4:35 am
If n is a positive integer less than 200 and 14n/60 is an integer, then n has how many different positive prime factors?

A. two

B. three

C. five

D. six

E. eight.



OA B
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by scoobydooby » Wed Apr 08, 2009 5:44 am
14n/60 is an integer
=>2*7*n/(2*2*3*5) is an integer
=> 7*n/(2*3*5) is an integer.
=> n must have atleast a 2, 3 and a 5. n cant have 7 as n<200

3 different prime numbers, hence B
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quick and easy

by artistocrat » Mon Apr 13, 2009 12:52 pm
(2*7*n)/(2*2*3*5), therefore the numerator needs n to contain 2*3*5 for result to be an integer.
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