Problem:
Find the smallest whole number that is larger than the sum
221β+331β+441β+551β?
Answer Choices:
A. 14
B. 15
C. 16
D. 17
E. 18
Solution:
The sum of the fractions adds between 1 and 121β to the sum of the whole numbers, which is 2+3+4+5=14. Thus the overall sum is between 15 and 1521β, so the answer is 16.
OR
Since
1<21β+41β+41β+51β<21β+31β+41β+51β<21β+21β+21β+21β=2
the sum of the fractions adds between 1 and 2 to the sum of the whole numbers, which is 2+3+4+5=14. Thus the overall sum is between 15 and 16, so the answer is 16.
OR
Approximate the fractions as decimals and add 2.5+3.33+4.25+5.2 which yields 15.28. Thus the answer is 16.
Answer: Cβ.
The problems on this page are the property of the MAA's American Mathematics Competitions