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

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Senior Manager
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If a and b are integers, is b even? (1) 3a + 4b is even (2) [#permalink]  09 Feb 2008, 12:48
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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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Manager
Joined: 02 Jan 2008
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Re: DS: Set-21, Q11 [#permalink]  09 Feb 2008, 13:13
1
KUDOS
C (and b is even)

(1) 3a + 4b is even: tells a is even, b can be both odd or even: INSUFF
(2) 3a + 5b is even: tells a and b can be odd/odd or even/even

A and B: a is even (from 1) and hence (from 2) b is even
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Re: DS: Set-21, Q11 [#permalink]  09 Feb 2008, 13:18

(1) 3a + 4b is even
ASsuming 3a + 4b is even. 3a and 4b could both be odd, or both be even.
Now, 4b cannot be odd, since any number multiplied by 4 is even.
Hence, b is even.
(2) 3a + 5b is even
Applying the above logic to b, b could be even or odd and it cannot be determined.
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Re: DS: Set-21, Q11 [#permalink]  09 Feb 2008, 13:24
bhatia_ash2002 wrote:

(1) 3a + 4b is even
ASsuming 3a + 4b is even. 3a and 4b could both be odd, or both be even.
Now, 4b cannot be odd, since any number multiplied by 4 is even.
Hence, b is even.

4b can't be odd but 'b' can be.

3a+4b = 3*4 + 4*3 = 24 (even)
Senior Manager
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Re: DS: Set-21, Q11 [#permalink]  09 Feb 2008, 13:26
Good explanation srp. +1

I kept thinking along the exact same lines but could not untangle out of the possibilities and went with B. Which was obviously wrong.

OA is C.
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Re: DS: Set-21, Q11   [#permalink] 09 Feb 2008, 13:26
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