1986 AMC 8 Problem 14

Attempt Problem 14 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).

14.

If 200≤a≤400200 \le a \le 400 and 600≤b≤1200,600 \le b \le 1200, then the largest value of the quotient ba\dfrac{b}{a} is
32\dfrac32
33
66
300300
600600
Answer: C
Concepts:inequalityoptimization
Small hint:
A quotient is largest when the numerator is as large as possible and the denominator as small as possible
Big hint:
Use the largest bb and the smallest aa
Solution:
The quotient ba\dfrac{b}{a} is largest with the biggest bb and smallest a,a, giving 1200200=6.\dfrac{1200}{200} = 6.
Thus, the correct answer is C .
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