Is the integer x divisible by 36?

[ektamatta]

15. Is the integer x divisible by 36?
(1) x is divisible by 12.
(2) x is divisible by 9.

[parallel_chase]

I think the answer is C.

There are two methods you can use for this kind of question.

First method:

Statement I. x is divisible by 12
36 is divisible by 12, 36 is also divisible by 36
48 is divisible by 12 but not divisible by 36.

Not Sufficient.

Statement II. x is divisible by 9
45 is divisible by 9, not by 36
72 is divisible by 9, also by 36

Not Sufficient.

Combining statement I & II
x is divisible by 12 as well as 9

36 is divisible by 36, 9 and 12
72 is divisible by 36, 9 and 12
108 is divisible by 36, 9 and 12

Second Method:

Find the prime factors of 36 = 2*2*3*3

Statement I.

Factors of 12 = 2*2*3 (notice we have one 3 missing) therefore some multiples of 12 will be multiples of 36 and some will not be.

Not Sufficient.

Statement II

Factors of 9 = 3*3 (we have two 2's missing)
Not Sufficient (same reasoning as above)

Combining Statement I & II
Factors of 9 and 12 together = 2*2*3*3*3 (notice we have one 3 extra)
Therefore every multiple of 12 and 9 together will also be a multiple of 36.

Hence C.

[ektamatta]

pretty good explanation. Thanks alot