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