1996 AHSME Problems/Problem 5
Contents
Problem
Given that , which of the following is the largest?
Solution 1
Assuming that one of the above fractions is indeed always the largest, try plugging in , since those are valid values for the variables given the constraints of the problem. The options become:
Simplified, the options are , respectively. Since is the only option that is greater than , the answer is .
Solution 2
To make a fraction large, you want the largest possible numerator, and the smallest possible denominator. Since and are the two largest numbers, they should go in the numerator as a sum. Since and are the smallest numbers, they should go in the denominator as a sum. Thus, the answer is .
You can compare option with every other fraction: all numerators are smaller than 's numerator, and all denominators are larger than 's denominator.
See also
1996 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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