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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]

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New post 17 Mar 2009, 21:18
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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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Re: Number property + DS [#permalink]

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New post 17 Mar 2009, 21:57
milind1979 wrote:
If a and b are integers, is b even?
(1) 3a + 4b is even.
(2) 3a + 5b is even.


C.

1) tells us that a is even, b can be either odd or even.
insuff.
2) tells us that a and be can be either odd or even.
Further tells us that if a is odd b must be odd But if a is even b must also be even.
insuff.

together
from 1. a is even ; from 2. if a is even => b must also be even.
suff.

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Re: Number property + DS [#permalink]

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New post 17 Mar 2009, 23:25
Got C as well.

1. b can be odd or even. Multiplying with 4 will always yield an even number
2. b can be odd, in which case a will be odd as well. b can be even, in which case a will be even.

Together: if b is odd, a is odd.

But when you take a as odd in the first equation, you will want 4b to be odd to satisfy the equation. That is clearly not possible. Hence b has to be even.

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Re: Number property + DS   [#permalink] 17 Mar 2009, 23:25
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If a and b are integers, is b even? (1) 3a + 4b is even. (2)

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