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AMC8每日一题(2000年真题#03)

2018-03-30
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2000 AMC 8 竞赛试题/第3题

Problem

How many whole numbers lie in the interval between 5/3and $2\pi?$

$\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 5 \qquad \text{(E)}\ \text{infinitely many}$

Solution

The smallest whole number in the interval is2 because5.3 is more than but less than 2. The largest whole number in the interval is6 because2π is more than6 but less than7 . There are five whole numbers in the interval. They are2,3,4,5,and 6, so the answer is （D）5.

Solution 2

We can approximate2π to 6. Now we approximate 5/3to2 . Now we list the integers between 2and6 including 2and6 : Hence, the answer is（D）