AMC8 1995

AMC8 1995 · Q5

AMC8 1995 · Q5. It mainly tests Vieta / quadratic relationships (basic), Fractions.

Find the smallest whole number that is larger than the sum $$2\frac{1}{2} + 3\frac{1}{3} + 4\frac{1}{4} + 5\frac{1}{5}.$$

求比以下和更大的最小整数 $$2\frac{1}{2} + 3\frac{1}{3} + 4\frac{1}{4} + 5\frac{1}{5}$$。

(A) 14 14

(B) 15 15

(D) 17 17

(E) 18 18

Answer

Correct choice: (C)

正确答案：（C）

Solution

The sum of the fractions adds between 1 and 2 to the sum of the whole numbers, which is $2 + 3 + 4 + 5 = 14$. Thus the overall sum is between 15 and 16, so the smallest whole number larger than the sum is 16.

分数之和给整数之和（$2 + 3 + 4 + 5 = 14$）增加了1到2之间。因此总和在15和16之间，所以比该和大的最小整数是16。

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