break down 135 into primes. 3^3*5umaa 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.
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)
