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Difference between revisions of "1994 AJHSME Problems/Problem 1"
 
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<math>\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}</math>
 
<math>\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}</math>
  
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==Solution==
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==Solution 1==
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C and D are the only answer choices where the numerator is close to half of the denominator. <math>\dfrac{3}{8}</math> is equal to .375 and <math>\dfrac{5}{12}</math> is equal to approximately .41. <math>\boxed{\text{D}}</math>
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C and D are the only answer choices where the numerator is close to half of the denominator. <math>\dfrac{3}{8} = .375</math> and <math>\dfrac{5}{12} \approx .41</math>. Thus the answer is <math>\boxed{\text{(D)}\ \frac{5}{12}}</math>
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==Solution 2==
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Multiply every answer choice by <math>24</math>, the [[LCM]] of all of the answer choices. This gives
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<math>\text{(A)}\ 8 \qquad \text{(B)}\ 6 \qquad \text{(C)}\ 9 \qquad \text{(D)}\ 10 \qquad \text{(E)}\ 7</math>
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of which <math>\boxed{D}</math> is the largest.
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==See Also==
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{{AJHSME box|year=1994|before=First <br /> Problem|num-a=2}}
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{{MAA Notice}}

Latest revision as of 11:47, 27 June 2023

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 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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