AB + CD = AAA, where AB and CD are two-digit numbers and AAA is a three digit number; A, B, C, and D are distinct positive integers. In the addition problem above, what is the value of C?
(A) 1
(B) 3
(C) 7
(D) 9
(E) Cannot be determined
Monday, December 10, 2007
Question # 6
Posted by Gaurav & Kunal at 10:20 PM
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5 Comments:
The value of C is (D) 9.
Becoz,
A = 1.
and A + C + 1(carried over) can make it 11.
Hence, C needs to be 9.
the reason you gave i am not clear with. anyways answer is recorded.
10A + B + 10C + D = 111A
10C = 101A - (B + D)
can only work if C= 9, since B+D can atmost be 17
Answer : 9 (D)
10A+B+CD=100A+10A+A
=> B+CD = 101A
Max(LHS) = 7+8*9 = 79
Min(RHS) = 101*1 = 101
=> A=1
Try B=2, CD=99, {C,D} does not exist
Try B=3, CD=98, C=9, D=8
Ans. (D)
one point for rushin shah for this question.
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