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 Options: A . &nbsp Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient B . &nbsp Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C . &nbsp EACH statement ALONE is sufficient. D . &nbsp BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. E . &nbsp Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

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

Question

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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