Question

If x, y are natural numbers, is the value of x+y an even number?
1. L.C.M of $x^2$ and y is 12
2. H.C.F of $y^2$ and x is 2

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• C. EACH statement ALONE is sufficient.
• D. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Answer 1

The correct option is B Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

(b)

Statement A implies (x, y) = {(2, 3), (2, 6), (1, 12), (2, 12)}

This implies x+y may be even or odd.

Statement (A) alone is not sufficient

Statement B: x, y = {(2, 2), (2, 6), (2, 8)...} i.e. X and y are both even numbers.

Statement B alone is sufficient.