Problem:
Which of the following is the largest?
Answer Choices:
A. 31
B. 41
C. 83
D. 125
E. 247
Solution:
Express all the choices as fractions using their least common denominator:
31=248,41=246,83=249,125=2410,247.
Thus, 5/12 is the largest.
OR
Express each choice as a decimal:
31=0.333…41=0.2583=0.375125=0.41666…247=0.291666…
Thus, 5/12 is the largest.
OR
All choices are less than 1/2, so the choice least distant from 1/2 will be the largest:
Fraction: Distance from 21:31,41,83,125,24761,41,81,121,245
Answer: D.
The problems on this page are the property of the MAA's American Mathematics Competitions