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If A, B, C, and D are integers such that A - C + B is even

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jamifahad
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If A, B, C, and D are integers such that A - C + B is even [#permalink] New post   Updated on: 19 Apr 2024, 04:02
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If \(A\), \(B\), \(C\), and \(D\) are integers such that \(A - C + B\) is even and \(D + B - A\) is odd, which of the following expressions must be odd?

A. \(A + D\)
B. \(B + D\)
C. \(C + D\)
D. \(A + B\)
E. \(A + C\)­


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C

Originally posted by jamifahad on 20 Sep 2011, 03:29.
Last edited by Bunuel on 19 Apr 2024, 04:02, edited 2 times in total.
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abhi6001
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Re: If A, B, C, and D are integers such that A - C + B is even [#permalink] New post   21 Sep 2011, 01:33
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Hi Jamifahad,

Even matrix method takes more than two mins in this problem since you have to jot down the even and odd values.

Try subtracting the equations
(A - C + B) - (D + B - A) = 2A-(C+D)

Even - Odd = Odd

So 2A-(C+D) is odd

2A is always even , so the subtrahend should always be odd, so C+D is odd.
Hope I am clear.
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Bunuel
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Re: If A, B, C, and D are integers such that A - C + B is even [#permalink] New post   19 Apr 2024, 04:03
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Official Solution:

If \(A\), \(B\), \(C\), and \(D\) are integers such that \(A - C + B\) is even and \(D + B - A\) is odd, which of the following expressions must be odd?

A. \(A + D\)
B. \(B + D\)
C. \(C + D\)
D. \(A + B\)
E. \(A + C\)


Subtract the first equation from the second:

\((D + B - A) - (A - C + B) = odd - even\);

\(C + D - 2A = odd\);

\(C + D = odd - 2A\);

\(C + D = odd - even\);

\(C + D = odd\).


Answer: C­
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BrentGMATPrepNow
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Re: If A, B, C, and D are integers such that A - C + B is even [#permalink] New post   03 Mar 2018, 09:10
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jamifahad wrote:
If A, B, C, and D are integers such that A - C + B is even and D + B - A is odd, which of the following expressions is always odd?

A. A + D
B. B + D
C. C + D
D. A + B
E. A + C


Given: A - C + B = EVEN and D + B - A = ODD
Add them to get: (A - C + B) + (D + B - A) = EVEN + ODD
Simplify: 2B + D - C = ODD
Since 2B is ALWAYS even, we get: EVEN + D - C = ODD
So: D - C = ODD - EVEN
This means: D - C = ODD
If D - C is ODD, then we know that one of the numbers is EVEN and the other number is ODD
If one of the numbers is EVEN and the other number is ODD, then C + D must also be ODD

Answer: C

Cheers,
Brent
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ritikajain1988
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If A, B, C, and D are integers such that A - C + B is even [#permalink] New post   05 Jul 2018, 16:48
CAN YOU PLEASE EXPLAIN WHAT IS THE MATRIX METHOD?
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BrentGMATPrepNow
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Re: If A, B, C, and D are integers such that A - C + B is even [#permalink] New post   05 Jul 2018, 16:57
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ritikajain1988 wrote:
CAN YOU PLEASE EXPLAIN WHAT IS THE MATRIX METHOD?


This video explains what it is:


Cheers,
Brent
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Re: If A, B, C, and D are integers such that A - C + B is even [#permalink]
05 Jul 2018, 16:57
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