Difference between revisions of "1986 AJHSME Problems/Problem 2"
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==Problem== | ==Problem== | ||
| − | Which of the following numbers has the largest reciprocal? | + | Which of the following numbers has the largest [[reciprocal]]? |
<math>\text{(A)}\ \frac{1}{3} \qquad \text{(B)}\ \frac{2}{5} \qquad \text{(C)}\ 1 \qquad \text{(D)}\ 5 \qquad \text{(E)}\ 1986</math> | <math>\text{(A)}\ \frac{1}{3} \qquad \text{(B)}\ \frac{2}{5} \qquad \text{(C)}\ 1 \qquad \text{(D)}\ 5 \qquad \text{(E)}\ 1986</math> | ||
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==Solution== | ==Solution== | ||
| − | For positive numbers, the larger the number, the smaller | + | For [[positive|positive numbers]], the larger the number, the smaller its reciprocal. Likewise, smaller numbers have larger reciprocals. |
Thus, all we have to do is find the smallest number. | Thus, all we have to do is find the smallest number. | ||
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==See Also== | ==See Also== | ||
| − | [[ | + | {{AJHSME box|year=1986|num-b=1|num-a=3}} |
| + | [[Category:Introductory Algebra Problems]] | ||
Revision as of 17:44, 19 May 2009
Problem
Which of the following numbers has the largest reciprocal?
Solution
For positive numbers, the larger the number, the smaller its reciprocal. Likewise, smaller numbers have larger reciprocals.
Thus, all we have to do is find the smallest number.
But which one is it? 
? or 
?
We see that 
, and 
, so obviously is smaller.
See Also
| 1986 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 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 | ||
