2000 AMC 8 Problems/Problem 3

Problem

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

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

Solution 1

The smallest whole number in the interval is $2$ because $5/3$ is more than $1$ but less than $2$ . The largest whole number in the interval is $6$ because $2\pi$ is more than $6$ but less than $7$ . There are five whole numbers in the interval. They are $2$ , $3$ , $4$ , $5$ , and $6$ , so the answer is $\boxed{\text{(D)}\ 5}$ .

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Solution 2

We can approximate $2\pi$ to $6$ . Now we approximate $5/3$ to $2$ . Now we list the integers between $2$ and $6$ including $2$ and $6$ : $2,3,4,5,6$ Hence, the answer is $\boxed{D}$

2000 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 2	Followed by Problem 4
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All AJHSME/AMC 8 Problems and Solutions

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2000 AMC 8 Problems/Problem 3

Contents

Problem

Solution 1

Solution 2

See Also