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.

1994 AJHSME (Problems • Answer Key • Resources)
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1994 AJHSME Problems/Problem 1

Contents

Problem

Solution 1

Solution 2

See Also