1986 AMC 8 Problem 2

Attempt Problem 2 of the 1986 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1986 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

2.

Which of the following numbers has the largest reciprocal?
13\dfrac13
25\dfrac25
11
55
19861986
Answer: A
Concepts:fraction
Small hint:
The reciprocal of a positive number is largest when the number itself is smallest
Big hint:
Compare the five numbers and find the smallest one
Solution:
A large positive number has a small reciprocal, and a small positive number has a large reciprocal. The smallest number listed is 13,\dfrac13, whose reciprocal 33 is the largest.
Thus, the correct answer is A .
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