Problem:
For how many integer values of x is β£2xβ£β€7Ο ?
Answer Choices:
A. 16
B. 17
C. 19
D. 20
E. 21
Solution:
From 3<Ο<3.142, it follows that
21=7β
3<7Ο<7β
3.142=21.994<22
Because x is an integer, the values for 2x that make the inequality true are β20,β18,β16,β¦,β2, 0,2,β¦,18, and 20 . Each of these corresponds to a unique value of x. There are (E)21β such values.
The problems on this page are the property of the MAA's American Mathematics Competitions