Is the integer X divisible by 36?

[quarks22]

Can somebody clarify this for me?

Is the integer X divisible by 36?
1. X is divisible by 12
2. X is divisible by 9

Isn't the answer "E" because we need to eliminate the redundant "3" when combining the prime boxes. This leaves just
two 2's and one 3 when combining prime boxes. Therefore, we dont know if x has two 2's and two 3's.

[saurav.raaj]

to find whether X is divisible by 36, X must be divisible by 4 and 9 (or infact 2 x 2 x 3 x 3, i.e. two 2's AND two 3's)

if X is divisible by 12, that means X = k1 x 12 = k1 x 2 x 2 x 3, we are still missing a 3 here. Not Sufficient.
(k1 is the other integer factor)

if X is divisible by 9, that means X = k2 x 9 = k2 x 3 x 3, we are still missing a 4 (or 2x 2) here. Not Sufficient.
(k2 is the other integer factor)

if we combine both, then we get get X divisible by 12 and 9 which means X = k3 x (12 ~ 2 x 2 x 3) x (9 ~ 3 x 3)
(k3 is the other integer factor)

we can re-write this:
X = k3 x (12 ~ 2 x 2 x 3) x (9 ~ 3 x 3)

as

X = k3 x 12 x 9 = k3 x 4 x 3 x 3 x 3 = k3 x 36 x 3

So we see, 36 emerges as one of the factors, while k3 x 3 is the other.

[JonathanSchneider]

Well shown.

To the first poster: in simpler terms, just be careful: 12 is 2*2*3. It seems you were forgetting about one of those 2's.