m and n

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umaa
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Topic: m and n
PostFri Jul 03, 2009 11:38 pm Reply with quote
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.
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ssmiles08
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PostSat Jul 04, 2009 2:46 pm Reply with quote
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. 3^3*5

for m*n 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 m*n has atleast three 3's in its product. which would make m*n/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)
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