# 1994 AJHSME Problems/Problem 1

## Problem

Which of the following is the largest?

$\text{(A)}\ \dfrac{1}{3} \qquad \text{(B)}\ \dfrac{1}{4} \qquad \text{(C)}\ \dfrac{3}{8} \qquad \text{(D)}\ \dfrac{5}{12} \qquad \text{(E)}\ \dfrac{7}{24}$

## Solution 1

C and D are the only answer choices where the numerator is close to half of the denominator. $\dfrac{3}{8} = .375$ and $\dfrac{5}{12} \approx .41$. Thus the answer is $\boxed{\text{(D)}\ \frac{5}{12}}$

## Solution 2

Multiply every answer choice by $24$, the LCM of all of the answer choices. This gives

$\text{(A)}\ 8 \qquad \text{(B)}\ 6 \qquad \text{(C)}\ 9 \qquad \text{(D)}\ 10 \qquad \text{(E)}\ 7$

of which $\boxed{D}$ is the largest.

## See Also

 1994 AJHSME (Problems • Answer Key • Resources) Preceded byFirst Problem Followed byProblem 2 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.