Problem:
If 991+993+995+997+999=5000−N, then N=
Answer Choices:
A. 5
B. 10
C. 15
D. 20
E. 25
Solution:
Each of the five numbers on the left side of the equation is approximately equal to 1,000 . Thus N can be found by computing the difference between 1,000 and each number, so N=9+7+5+3+1=25.
OR
Since
991+993+995+997+999​=(1000−9)+(1000−7)+(1000−5)+(1000−3)+(1000−1)=5000−(9+7+5+3+1)=5000−25​
it follows that N=25.
Answer: 25​.
The problems on this page are the property of the MAA's American Mathematics Competitions