varun289 wrote:If m is an integer, is
m102
an integer?

99 is a factor of 165m.
34 is a factor of 7m

can you please post the complete question. m102 is an integer doesn't make sense. Is it m/102?

I know this one - it should read "Is m/102 an integer" or "Is m divided by 102 an integer).

solving for m/102

102 = 2* 3 * 17

so if m has at least one 2, one 3 and one 17 in its factor then m is divisible by 102.

statement 1

165 = 5 * 3 * 11 and 99 = 3 * 3 * 11

so when we say 99 is a factor of 165 * M we mean that 165 *M will have at least this 3 * 3 * 11. now we know that 165 has one 3 and one 11 as a factor so other 3 of 99 is coming from M.

we have 3 as one of the factor of M but we don't know that whether 2 and 17 are factors of M.

Not Sufficient.


Statement 2:

34 = 2 * 17

for 34 to be a factor of 7 * M , M must has one 2 and one 17 as its factor.

but we don't know whether 3 is a factor of M

Not sufficient.

now combing both statement

from 1st statement we know that 3 is the factor of M and from 2nd statement we know that 2 and 17 are factor of M. hence m is divisible by 102.

Option C

m is INTEGER, is m/102 and INTEGER??

102 = 2 * 3 * 17
does m have factors 2, 3 and 17?

1. 99 is factor of 165m => 3 * 3 * 11 is factor of 3 * 5 * 11 * m
Hence m must be a factor of 3 (but we dont know about whether m is a factor of 2 and 17 or not)
hence INSUFFICIENT

2. 34 is factor of 7m => 2 * 17 is factor of 7 * m. this implies m must have as its factors a 2 and a 17. However we dont know whether m has a 3 or not. There could be a 3 or there may not be a 3.
Hence INSUFFICIENT.

Together 1 + 2: from 1 we know m has a 3 and from 2 we know m has a 2 and a 17
hence m is atleast 2 * 3 * 17 ( that are all the factors common to 102)
Hence m / 102 is an integer
SUFFICIENT
Answer C