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

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Joined: 29 Aug 2007
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If a and b are integers, is b even? (1) 3a + 4b is even (2) [#permalink]  31 Oct 2007, 20:26
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11. If a and b are integers, is b even?

(1) 3a + 4b is even
(2) 3a + 5b is even
Senior Manager
Joined: 27 Aug 2007
Posts: 253
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Ans is C,

1. both should be either even or odd,
4b cannot be odd, so both of them should be even, than 3a is even and 4b is also even and b can be either odd or even. So INSUFF

2. again the same rule, both odd or borth even. again b can be either odd or even INSUFF

Together SUFF because only difference 4b and 5b only when b is even

Ans: C
VP
Joined: 08 Jun 2005
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I second (C)

o = odd
e = even

statement I

3e+4e = e ---> true
3o+4o = e ---> false
3e+4o = e ---> true
3o+4e = e ---> false

insufficient

statement II

3e+5e = e ---> true
3o+5o = e ---> true
3e+5o = e ---> false
3o+5e = e ---> false

insufficient

both statements

3e+4e = e ---> true
3e+5e = e ---> true

sufficient

CEO
Joined: 29 Mar 2007
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Re: DS: ODD or EVEN [#permalink]  01 Nov 2007, 15:42
GMAT TIGER wrote:
11. If a and b are integers, is b even?

(1) 3a + 4b is even
(2) 3a + 5b is even

C. No need for calculations really.

1: notice that 3a+4b could be E+E and... thats it. 3a CANNOT be odd or 3a+4b would be odd. So keep that in mind from S1 that a must be even. (dont carry it to S2 though )

2: 3a+5b. we can have E+E or O+O. so this is insuff.

Now together we know that a is even. So 5b must be even or 3a+5b would not be even. thus B must be even.
Re: DS: ODD or EVEN   [#permalink] 01 Nov 2007, 15:42
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