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 (ProblemsAnswer KeyResources)
Preceded by
First
Problem
Followed by
Problem 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

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