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11 Aug 2021, 04:17
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The two red portions contradict each other:
Whereas C=5 in the first red statement, C=9 in the second.
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29 Mar 2022, 04:29
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Official Explanation:
First, note that A, B, C, and D have to be digits between 1 and 9 (and the problem does not prevent some letters from having the same value).
The two rightmost columns both contain C + B = D. From that information, you can deduce that B + C < 9. (If B + C were 10 or more, then the rightmost column would “carry over” into the next column, making the tens digit into D + 1 rather than D.)
Next, A + B = C. A larger value of C, then, will reduce B (because B + C < 9) and therefore increase A (because A + B = C).
Since the questions asks to maximize the product for A and B, consider only the cases in which B + C = 9. Further, since A + B = C, you also know that B must be less than C. (Not sure why? Test a couple of real numbers to figure it out.) That leaves only a few cases, so write them out:
If B = 1 and C = 8, then A = 7. In this case, the product of A and B is 7.
If B = 2 and C = 7, then A = 5. In this case, the product of A and B is 10.
If B = 3 and C = 6, then A = 3. In this case, the product of A and B is 9.
If B = 4 and C = 5, then A = 1. In this case, the product of A and B is 4.
That’s all of the possible cases. The largest possible product is 10.
The correct answer is B.
First, note that A, B, C, and D have to be digits between 1 and 9 (and the problem does not prevent some letters from having the same value).
The two rightmost columns both contain C + B = D. From that information, you can deduce that B + C < 9. (If B + C were 10 or more, then the rightmost column would “carry over” into the next column, making the tens digit into D + 1 rather than D.)
Next, A + B = C. A larger value of C, then, will reduce B (because B + C < 9) and therefore increase A (because A + B = C).
Since the questions asks to maximize the product for A and B, consider only the cases in which B + C = 9. Further, since A + B = C, you also know that B must be less than C. (Not sure why? Test a couple of real numbers to figure it out.) That leaves only a few cases, so write them out:
If B = 1 and C = 8, then A = 7. In this case, the product of A and B is 7.
If B = 2 and C = 7, then A = 5. In this case, the product of A and B is 10.
If B = 3 and C = 6, then A = 3. In this case, the product of A and B is 9.
If B = 4 and C = 5, then A = 1. In this case, the product of A and B is 4.
That’s all of the possible cases. The largest possible product is 10.
The correct answer is B.
21 Aug 2023, 15:55
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C+B = D =< 9
A+B = C
Therefore,
2B+A =<9
2(1) + 7 =< 9 -> 1*7 = 7
2(2) + 5 =< 9 -> 2*5 = 10
2(3) + 3 =< 9 -> 3*3 = 9
2(4) + 1 =< 9 -> 4*1 = 4
Can't go further since 2(5) > 9
A+B = C
Therefore,
2B+A =<9
2(1) + 7 =< 9 -> 1*7 = 7
2(2) + 5 =< 9 -> 2*5 = 10
2(3) + 3 =< 9 -> 3*3 = 9
2(4) + 1 =< 9 -> 4*1 = 4
Can't go further since 2(5) > 9
