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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]  28 Nov 2005, 07:27
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If a and b are integers, is b even?
(1) 3a + 4b is even.
(2) 3a + 5b is even.
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Tanmoi.

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Re: Integers DS [#permalink]  28 Nov 2005, 07:40
Tanmoi wrote:
If a and b are integers, is b even?
(1) 3a + 4b is even.
(2) 3a + 5b is even.

1) Says that a has to be even. B can be odd/even -- insuff
2) Says that either a odd and b odd or a even and b even -- insuff

Taking 1 and 2 together, we know that a is even so b has to be even.

Ans = C
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If 3a + 4b is even and 3a + 5b is even, then

3(2) x 4(4) = 22 (even)
3(2) x 4(5) = 26 (even)

3(3) + 5(5) = 34 (even)
3(2) + 5(4) = 26 (even)

So even if both are taken together, how can we say b is even? Pls explain. Thanks.
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Tanmoi.

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Re: Integers DS [#permalink]  28 Nov 2005, 16:47
Tanmoi wrote:
If a and b are integers, is b even?
(1) 3a + 4b is even.
(2) 3a + 5b is even.

adding them together yields: 6a+9b as an even. Since 6a is even ----> 9b is even ---> b is even becoz even-even=even
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(1) We're told 3a + 4b = even.
4b is an even number, so 3a must be even. Therefore a must be even. However, we can't tell if b is odd or even.

(2) We're 3a + 5b = even. 3a and 5b both can be odd, or both can be even. So we can't tell what are a and b.

Using (1) and (2), we know a is even, so 3a is even. so 5b must be even and b must be even.

Ans: C
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Re: Integers DS [#permalink]  28 Nov 2005, 19:04
C

If a and b are integers, is b even?
(1) 3a + 4b is even.
a +2a+4b= even ( means a is even ) but no info about b NS

(2) 3a + 5b is even
a+b+2a+4b = even
a+b= even
NS can not conclude b even

taking together from 1 a is even for a+b to be even b has to be even .
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Re: Integers DS [#permalink]  29 Nov 2005, 03:59
Tanmoi wrote:
If a and b are integers, is b even?
(1) 3a + 4b is even.
(2) 3a + 5b is even.

I would go with C. Here is my working.

3a+4b is even and 3a+5b is even
Subtracting 2 from 1
(3a+5b)-(3a+4b) = b
even - even = even
so b should be even.
Re: Integers DS   [#permalink] 29 Nov 2005, 03:59
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