m and n

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umaa
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Topic: m and n

Sat Jul 04, 2009 12:38 am

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If m and n are integers, and m is a multiple of 5, is mn a multiple of 135?

1. m is a multiple of 3.

2. n is a multiple of 9

OA is C

Explanation pls.

ssmiles08
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Sat Jul 04, 2009 3:46 pm

umaa wrote: If m and n are integers, and m is a multiple of 5, is mn a multiple of 135? 1. m is a multiple of 3. 2. n is a multiple of 9 OA is C Explanation pls. break down 135 into primes. 3^35 for mn to be divisible by 135, there must be atleast three 3's and one 5. we know that one 5 is satisfied by m being a multiple of 5. 1) m is a multiple of 3. m can have one 3, two 3's or three 3's. (m = 3, 9, 27... and so on) we have no information on how many multiples of 3 n has. INSUFF. 2) n has atleast two 9's. same scenario here, m can equal 9 or 27 or so on. No information on m. together. we can conclude that mn has atleast three 3's in its product. which would make mn/135 an integer. m*n would be a multiple of 135 since m is a multiple of 15 and n is a multiple of 9. (C)