prasannar wrote:

If a and b are integers, is b even?

(1) 3a + 4b is even

(2) 3a + 5b is even

(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) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

(D) EACH statement ALONE is sufficient.

(E) Statements (1) and (2) TOGETHER are NOT sufficient.

Is b even?

Statement (1) alone 3a + 4b = even. Since any number multiply by an even number, in this case 4, must be even. b can be odd or even. 3a cannot be odd since only even + even = even. Not sufficient. Eliminate A and D.

Statement (2) alone 3a +5b = even. Again, any number multiply by an odd number will be can be odd or even. Thus, a and b can be odd or even numbers.

However, only odd + odd = even or even + even = even (even + odd = odd). Since 5b can be odd or even. Not sufficient. Eliminate B.

Statement (1) and (2) together. From statement (1), b can be odd or even. From statement (2), b can also be odd or even. Thus, we can't be certain if b is odd or even. Eliminate C.

Ans:

E
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Jimmy Low, Frankfurt, Germany

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