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]

24 Dec 2005, 22:43

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If a and b are integers, is b even?
(1) 3a + 4b is even.
(2) 3a + 5b is even.

I got the answer, but it took some time working out! Wanted to check any shorter methods!
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Re: DS: Even integer [#permalink]

24 Dec 2005, 23:51

JAI HIND wrote:

If a and b are integers, is b even?
(1) 3a + 4b is even.
(2) 3a + 5b is even.

I got the answer, but it took some time working out! Wanted to check any shorter methods!

My answer is C

For a sum of two numbers to be even..two numbers can either

EVEN + EVEN
ODD + ODD

(1) 3a + 4b is even ==> 4b cannot be odd so it must be the even + even combination. B could be odd or even ==> Insufficient

(2) 3a + 5b is even ==> Could be EVEn + EVEN, ODD + ODD combo. Insufficient

(1) + (2) ==> From (1), we know that 3a must be even...so in (2) 5b must be even as well ==> b = even
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Re: DS: Even integer [#permalink]

25 Dec 2005, 01:14

TeHCM wrote:

JAI HIND wrote:

If a and b are integers, is b even?
(1) 3a + 4b is even.
(2) 3a + 5b is even.

I got the answer, but it took some time working out! Wanted to check any shorter methods!

I got C. I did the same way as done by TeHCM
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Re: DS: Even integer [#permalink]

25 Dec 2005, 23:50

JAI HIND wrote:

If a and b are integers, is b even?
(1) 3a + 4b is even.
(2) 3a + 5b is even.

I got the answer, but it took some time working out! Wanted to check any shorter methods!

From 1 we get 3a+4b = 0 mod 2
From 2 we get 3a+5b = 0 mod 2

Subtracting 2 from 1 we get b = 0 mod 2 hence C.

Re: DS: Even integer [#permalink] 25 Dec 2005, 23:50

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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)

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

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