题目信息
Five integers between 10 and 99, inclusive, are to be formed by using each of the ten digits exactly once in such a way that the sum of the five integers is as small as possible. What is the greatest possible integer that could be among these five numbers?
A:98
B:91
C:59
D:50
E:37
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已选答案：
正确答案：
C:59
Arithmetic Place value
Note that 0 cannot be the tens digit of an integer between 10 and 99, inclusive. In order for the sum of the five integers to be as small as possible, their tens digits should be the five smallest remaining digits (that is, 1, 2, 3, 4, and 5), leaving the digits 0, 6, 7, 8, and 9 to be used as the ones digits. Let a, b, c, d, and e represent distinct digits chosen from the digits 0, 6, 7, 8, and 9. The sum of the five integers formed in this way is as small as possible and equals (10 + a) + (20 + b) + (30 + c) + (40 + d) + (50 + e) = 150 + (a + b + c + d + e) = 150 + 30 = 180 regardless of how the digits 0, 6, 7, 8, and 9 are assigned to a, b, c, d, and e. By assigning 9 to e, it follows that one of the integers could be 59. Therefore, 59 is the greatest possible integer among the five integers whose sum is 180.
The correct answer is C.
Note that 0 cannot be the tens digit of an integer between 10 and 99, inclusive. In order for the sum of the five integers to be as small as possible, their tens digits should be the five smallest remaining digits (that is, 1, 2, 3, 4, and 5), leaving the digits 0, 6, 7, 8, and 9 to be used as the ones digits. Let a, b, c, d, and e represent distinct digits chosen from the digits 0, 6, 7, 8, and 9. The sum of the five integers formed in this way is as small as possible and equals (10 + a) + (20 + b) + (30 + c) + (40 + d) + (50 + e) = 150 + (a + b + c + d + e) = 150 + 30 = 180 regardless of how the digits 0, 6, 7, 8, and 9 are assigned to a, b, c, d, and e. By assigning 9 to e, it follows that one of the integers could be 59. Therefore, 59 is the greatest possible integer among the five integers whose sum is 180.
The correct answer is C.
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