If x, y are natural numbers, is the value of x+y an even number? 1. L.C.M of x2

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If x, y are natural numbers, is the value of x+y an even number?
1. L.C.M of x² and y is 12
2. H.C.F of y² and x is 2

Options:

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.

E . Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Answer: Option B
:
B
(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.

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