ABC+BCB= CDD
In the addition shown above, A, B, C, and D represent the nonzero digits of three 3-digit numbers. What is the largest possible value of the product of A and B ?
a.8
b.10
c.12
d.14
e.18
ABC
BCB
CDD
To MAXIMIZE A and B, we must MAXIMIZE the value of C.
Case 1: C=9
AB
9
B9B
9DD
Here, B=0, which violates the constraint that B is nonzero.
Case 2: C=8
AB
8
B8B
8DD
Here, B=1, implying that A=7.
In this case, A*B = 7*1, which is not among the answer choices.
Case 3: C=7
AB
7
B7B
7DD
Here, it's possible that B=2, implying that A=5.
In this case, A*B = 5*2 = 10.
Case 4: C=6
AB
6
B6B
6DD
Here:
If B=3, then A=3, in which case A*B = 3*3 = 9.
If B=2, then A=4, in which case A*B = 4*2 = 8.
If B=1, then A=5, in which case A*B = 5*1 = 6.
At this point, we can see that the maximum possible product is yielded by Case 3:
A*B = 5*2 = 10.
The correct answer is
B.
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