Problem:
What is the correct ordering of the three numbers 195​,217​, and 239​, in increasing order?
Answer Choices:
A. 239​<217​<195​
B. 195​<217​<239​
C. 239​<195​<217​
D. 195​<239​<217​
E. 217​<195​<239​
Solution:
Using a common denominator, 195​=399105​ and 217​=399133​, so 195​<217​.
Also 217​=483161​ and 239​=483189​, so 217​<239​.
OR
Comparing each fraction, 217​=31​,195​<155​=31​, and 239​>279​=31​, so the correct increasing order is 195​<217​<239​.
Answer: B​.
The problems on this page are the property of the MAA's American Mathematics Competitions