Problem:
Three positive integers are equally spaced on a number line. The middle number is and the largest number is times the smallest number. What is the smallest of these three numbers?
Answer Choices:
A.
B.
C.
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E.
Solution:
Since one of the outer numbers is times the other, we can make one of the numbers and the other be . Since the numbers are equally spaced, the middle number is the average of the outer two. This means the average of and is , so . This simplifies to , which means , so .
Our outer numbers therefore are and , so the smaller one is .
Thus, the answer is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions