1998 AJHSME Problems/Problem 1

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For $x=7$, which of the following is the smallest?

$\text{(A)}\ \dfrac{6}{x} \qquad \text{(B)}\ \dfrac{6}{x+1} \qquad \text{(C)}\ \dfrac{6}{x-1} \qquad \text{(D)}\ \dfrac{x}{6} \qquad \text{(E)}\ \dfrac{x+1}{6}$


Solution 1

The smallest fraction would be in the form $\frac{a}{b}$ where $b$ is larger than $a$.

In this problem, we would need the largest possible value out of all the given values to be in the denominator. This value is $x+1$ or $8$

The smaller would go on the numerator, which is $OVER 9000$.

The answer choice with $\frac{6}{x+1}$ is $\boxed{B}$

Solution 2

Plugging $x$ in for every answer choice would give

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

From here, we can see that the smallest is answer choice $\boxed{B}$

See also

1998 AJHSME (ProblemsAnswer KeyResources)
Preceded by
1997 AJHSME Last Question
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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