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# If a and b are integers, is b even? (1) 3a + 4b is even (2)

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If a and b are integers, is b even? (1) 3a + 4b is even (2) [#permalink]  10 May 2008, 02:23
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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.
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Director
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Re: DS: Even [#permalink]  10 May 2008, 05:13
from 1) we know that either 3a and 4b are both even or both odd, however 4b can never be odd. This leaves us with 4b = even, but b can be either even or odd. so insuff

from 2) we know that either 3a and 5b are both even or both odd. If 5b is even, b is even. If 5b is odd, b is odd. insuff

from 1)2) we know that 3a being odd is never a possibility, so 4b and 5b BOTH are even, hence b = even

ans = C
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Re: DS: Even [#permalink]  10 May 2008, 06:15
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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Re: DS: Even [#permalink]  10 May 2008, 06:29
Quote:
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.

yes but you have to dig a bit deeper. from statement 1) we can see that 3a has to be even, since 4b will ALWAYS be even. given that fact, 3a in statement 2) has to be even too. and if 3a in statement 2) is even, 5b in statement 2) has to be even, hence b has to be even..

C) for me
Re: DS: Even   [#permalink] 10 May 2008, 06:29
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# If a and b are integers, is b even? (1) 3a + 4b is even (2)

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