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If a and b are integers, is b even?

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If a and b are integers, is b even? [#permalink] New post 24 Jan 2008, 03:46
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It has taken me 4+ min to solve. I'm sure there is a method to solve those even\odd DS's.
can't imagine sitting on those Q's more than 2.5 min each in the real GMAT. would any of you people like to share a method for those kind of Q's :?:

If a and b are integers, is b even?

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

I'm less interested in the final answer, more in the way so please explain.

asalways, OA will follow.
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Re: DS:SET 21 #11 [#permalink] New post 24 Jan 2008, 03:58
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30 sec. all in mind.

1. 3a + 4b is even
1.1. even+even=even ==> a - even, b - even or odd
1.2. odd+odd=even ==> does not work because 4b is always even
insuff.

2. 3a + 5b is even
2.1. even+even=even ==> a - even, b - even
2.2. odd+odd=even ==> a - odd, b - odd
insuff.

1&2. a is even. Therefore, b can be only even.
suff.
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Re: DS:SET 21 #11 [#permalink] New post 24 Jan 2008, 03:55
GGUY wrote:
It has taken me 4+ min to solve. I'm sure there is a method to solve those even\odd DS's.
can't imagine sitting on those Q's more than 2.5 min each in the real GMAT. would any of you people like to share a method for those kind of Q's :?:

If a and b are integers, is b even?

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

I'm less interested in the final answer, more in the way so please explain.

asalways, OA will follow.


1.4b is even, no matter what b is!, and 3a+4b is even, so a must be even. No fixed about b, -> not sufficient

2. 3a + 5b even
2.1 even +even =even
2.2 odd +odd = even
so b can be even or odd --> not sufficient

1 and 2 combined is sufficient
from 1, we know a is even, so 3a must be even, and 3a +5b is even, therefore, b must be even --> sufficient

C
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Re: DS:SET 21 #11 [#permalink] New post 25 Jan 2008, 12:12
walker wrote:
C
30 sec. all in mind.
i wish i had that (in my mind) :wink:
thanks all OA is C

walker +1 (thats the 3rd or 4th kodus I have given you, go buy yourself something nice)
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Re: DS:SET 21 #11 [#permalink] New post 25 Jan 2008, 12:51
:) thanks for the question +1
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Re: DS:SET 21 #11   [#permalink] 25 Jan 2008, 12:51
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