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 $\boxed{\text{(D)}\ 5}$. slayy bestie

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 $\boxed{D}$

See Also

2000 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 2
Followed by
Problem 4
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions

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