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# if A B C D represents a different digit what is the value

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Director
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if A B C D represents a different digit what is the value [#permalink]

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25 Jan 2005, 15:50
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if A B C D represents a different digit what is the value of A

2 A
+ B 2
_______

D 2 C
_______
Director
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25 Jan 2005, 16:02
A + 2 = C
or A + 2-10 = C -(1)

B+ 2 = 2
or
B+2 + 1 -10 = 2 -(2)

Since carry D is non zero,
B = 9

=>
A = 8, C=0, D=1
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25 Jan 2005, 21:17
nocilis good job

Actually, I am little confused can you clarify as to why can't value of B be 8? & also how you can subtract 10 only on one side?. Thanks
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Praveen

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25 Jan 2005, 22:15
praveen_rao7 wrote:
nocilis good job

Actually, I am little confused can you clarify as to why can't value of B be 8? & also how you can subtract 10 only on one side?. Thanks

if A B C D represents a different digit what is the value of A

2A
+ B2
______
D 2 C

there are two reasons. first, the unit digit of sum of B and 2 is already given as 2. to have 2 as unit digit of the sum of B+2, we have to have 9 as the value of B.
Second, we know A,B,C, and D, all, are different digits and D is 1 (because no one digit two integers have sum more than 19) and it must be 1. when D is 1, then 2+A must not be 11 and can not be more than 11. to have B+2 as 12, A+2 must be two digit integer which can only be possible when A is 8. when A is 8, B cannot be 8 because A,B,C, and D, all, numbers/integers are different digits . therefore B must be 9.
25 Jan 2005, 22:15
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