AMC8 1994

AMC8 1994 · Q8

AMC8 1994 · Q8. It mainly tests Basic counting (rules of product/sum), Digit properties (sum of digits, divisibility tests).

For how many three-digit whole numbers does the sum of the digits equal 25?

三位数中有多少个各位数字之和等于25？

(A) 2 2

(B) 4 4

(D) 8 8

(E) 10 10

Answer

Correct choice: (C)

正确答案：（C）

Solution

Since the sum of the three digits must equal 25 and 8+8+8 = 24, it follows that at least one of the digits must be a 9. If only one digit is 9, then the other two digits add up to 16 and are each 8. If two digits are 9, then the other digit is 7. There are six numbers: 988, 898, 889, 997, 979, 799.

三位数字之和必须等于25，且 $8+8+8 = 24$，因此至少有一个数字是9。如果只有一个9，则另外两个数字之和为16，每个是8。如果两个9，则另一个数字是7。有六个这样的数：988、898、889、997、979、799。

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