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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

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

## 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.

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