Problem:
Let W,X,Y and Z be four different digits selected from the set
{1,2,3,4,5,6,7,8,9}.
If the sum XW+ZY is to be as small as possible, then XW+ZY must equal
Answer Choices:
A. 172
B. 173
C. 7217
D. 7225
E. 3613
Solution:
Small numerators and large denominators yield small fractions. Use 1 and 2 for numerators and 8 and 9 for denominators to obtain the smallest fractions, then compare the sums
81+92=729+16=7225 and 91+82=728+18=7226
to see that 7225 is the answer.
Note. Analyzing the sums yields 81+91+91 which is smaller than 91+81+81.
Answer: D.
The problems on this page are the property of the MAA's American Mathematics Competitions