Problem:
How many integer values satisfy β£xβ£<3Ο ?
Answer Choices:
A. 9
B. 10
C. 18
D. 19
E. 20
Solution:
Since 3Οβ9.42, we multiply 9 by 2 for the integers from 1 to 9 and the integers from β1 to β9 and add 1 to account for 0 to get (D) 19β .
OR
β£xβ£<3ΟβΊβ3Ο<x<3Ο. Since Ο is approximately 3.14,3Ο is approximately 9.42 . We are trying to solve for β9.42<x<9.42, where xβZ. Hence, β9.42<x<9.42βΉβ9β€xβ€9, for xβZ. The number of integer values of x is 9β(β9)+1=19. Therefore, the answer is (D) 19β .
The problems on this page are the property of the MAA's American Mathematics Competitions