2000 AMC 8 Problem 3

Attempt Problem 3 of the 2000 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2000 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

3.

How many whole numbers lie in the interval between 53\frac{5}{3} and 2π?2\pi?
22
33
44
55
infinitely many
Answer: D
Concepts:counting integers in a rangeestimation
Small hint:
Locate 53\frac{5}{3} and 2π2\pi between whole numbers
Big hint:
Count the whole numbers strictly inside the interval
Solution:
The smallest whole number greater than 53\frac{5}{3} is 2.2. The greatest whole number less than 2π2\pi is 6.6.
The whole numbers within this range are 2,3,4,5,6. 2, 3, 4, 5, 6.
Thus, D is the correct answer.
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