Difference between revisions of "2000 AMC 8 Problems/Problem 3"
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The smallest whole number in the interval is <math>2</math> because <math>5/3</math> is more than <math>1</math> but less than <math>2</math>. The largest whole number in the interval is <math>6</math> because <math>2\pi</math> is more than <math>6</math> but less than <math>7</math>. There are five whole numbers in the interval. They are <math>2</math>, <math>3</math>, <math>4</math>, <math>5</math>, and <math>6</math>, so the answer is <math>\boxed{\text{(D)}\ 5}</math>. | The smallest whole number in the interval is <math>2</math> because <math>5/3</math> is more than <math>1</math> but less than <math>2</math>. The largest whole number in the interval is <math>6</math> because <math>2\pi</math> is more than <math>6</math> but less than <math>7</math>. There are five whole numbers in the interval. They are <math>2</math>, <math>3</math>, <math>4</math>, <math>5</math>, and <math>6</math>, so the answer is <math>\boxed{\text{(D)}\ 5}</math>. | ||
+ | ==Solution 2== | ||
+ | We can approximate <math>2\pi</math> to <math>6</math>. Now we approximate <math>5/3</math> to <math>2</math>. Now we list the integers between <math>2</math> and <math>6</math>: | ||
+ | <cmath>2,3,4,5,6</cmath> | ||
+ | Hence, the answer is <math>\boxed{D}</math> | ||
==See Also== | ==See Also== |
Revision as of 19:55, 8 February 2016
Contents
[hide]Problem
How many whole numbers lie in the interval between and ?
Solution
The smallest whole number in the interval is because is more than but less than . The largest whole number in the interval is because is more than but less than . There are five whole numbers in the interval. They are , , , , and , so the answer is .
Solution 2
We can approximate to . Now we approximate to . Now we list the integers between and : Hence, the answer is
See Also
2000 AMC 8 (Problems • Answer Key • Resources) | ||
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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