What is the value of number X?

Statement 1

Lets write the prime factorisation of 36. 36 = 2^2 * 3^2. And 4 = 2^2.
Since HCF of X and 36 is 2^2, it means X contains at least two 2's, But X cannot contain any 3's (else 3 would have also come into HCF).
Thus this tells us that X has at least 2^2 (or could have higher powers of 2), does NOT contain any 3, but might contain any other prime number than 3.

But this doesnt give us a unique value of X. Not sufficient.


Statement 2

36 = 2^2 * 3^2 and 72 = 2^3 * 3^2.
Since LCM contains product of all prime numbers with their highest powers, it means X must have three 2's in its prime factorisation (else its not possible for LCM to contain 2^3), and X CAN have only one or two 3's in its prime factorisation (because if it contained any more powers of 3, then LCM would have reflected that). And also X cannot contain any other prime number than 2 & 3 (else LCM would have reflected that).

Thus X could be either 2^3 or 2^3 * 3 or 2^3 * 3^2. Not a unique value of X. so Not Sufficient.


Combining the two statements,
X has exactly three 2's (from second statement)
X has no 3's at all (from first statement)
X does not contain any other prime number except 2 & 3 (from second statement)

Thus, X = 2^3 or 8. Sufficient.

Hence C answer