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the correctly worked addition

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the correctly worked addition

by sanju09 » Sat Feb 04, 2012 4:31 am
0 3 A
+ B 5
-------
C D 4
-------

In the correctly worked addition given above, A, B, C, and D represent distinct non-zero digits. What is the value of B + D?
(1) B is even.
(2) D is even.


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Source: — Data Sufficiency |

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by Anurag@Gurome » Sat Feb 04, 2012 5:07 am
sanju09 wrote:0 3 A
+ B 5
-------
C D 4
-------

In the correctly worked addition given above, A, B, C, and D represent distinct non-zero digits. What is the value of B + D?
(1) B is even.
(2) D is even.


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A = 9
Then 1 + 3 + B = D or 4 + B = D

(1) B is even implies D is also even, since 4 + even = even.
If B = 2, D = 6, which is not possible as C will be zero in this case.
If B = 4, D = 8, which is not possible as C will be zero in this case.
If B = 6, D = 0, with a carry over of 1, which implies C = 1, which is not possible as D will be zero in this case.
If B = 8, D = 2 with a carry over of 1, which implies C = 1 is the only possibility.
So, B + D = 10; SUFFICIENT.

(2) D is even implies B is also even, since 4 + even = even.
Same as above; SUFFICIENT.

The correct answer is D.
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