Difference between revisions of "2021 AMC 10B Problems/Problem 1"
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<math>\textbf{(A)} ~9 \qquad\textbf{(B)} ~10 \qquad\textbf{(C)} ~18 \qquad\textbf{(D)} ~19 \qquad\textbf{(E)} ~20</math> | <math>\textbf{(A)} ~9 \qquad\textbf{(B)} ~10 \qquad\textbf{(C)} ~18 \qquad\textbf{(D)} ~19 \qquad\textbf{(E)} ~20</math> | ||
− | ==Solution== | + | ==Solution 1== |
Since <math>3\pi</math> is about <math>9.42</math>, we multiply 9 by 2 and add 1 to get <math> \boxed{\textbf{(D)}\ ~19} </math>~smarty101 | Since <math>3\pi</math> is about <math>9.42</math>, we multiply 9 by 2 and add 1 to get <math> \boxed{\textbf{(D)}\ ~19} </math>~smarty101 | ||
Revision as of 01:45, 12 February 2021
Contents
[hide]Problem
How many integer values of satisfy ?
Solution 1
Since is about , we multiply 9 by 2 and add 1 to get ~smarty101
Solution 2
There are two cases here.
When and So then
When and So then . Dividing by and flipping the sign, we get
From case 1 and 2, we need . Since is an integer, we must have between and . There are a total of
-PureSwag
Solution 3
. Since is approximately , is approximately . We are trying to solve for , where . Hence, , for . The number of integer values of is . Therefore, the answer is .
~ {TSun} ~
2021 AMC 10B (Problems • Answer Key • Resources) | ||
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All AMC 10 Problems and Solutions |