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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]

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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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JAI HIND!

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24 Dec 2005, 23:51
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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!

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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Joined: 20 Nov 2005
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Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008

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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!

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

I got C. I did the same way as done by TeHCM
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

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Senior Manager
Joined: 15 Apr 2005
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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.

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Re: If a and b are integers, is b even? (1) 3a + 4b is even. (2) [#permalink]

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08 Sep 2017, 04:29
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If a and b are integers, is b even? (1) 3a + 4b is even. (2)   [#permalink] 08 Sep 2017, 04:29
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