Difference between revisions of "1986 AJHSME Problems/Problem 2"
5849206328x (talk | contribs) (New page: ==Problem== 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...) |
|||
| Line 7: | Line 7: | ||
==Solution== | ==Solution== | ||
| − | {{ | + | For positive numbers, the larger the number, the smaller it's reciprocal. Likewise, smaller numbers have larger reciprocals. |
| + | |||
| + | Thus, all we have to do is find the smallest number. | ||
| + | |||
| + | But which one is it? <math>\frac{1}{3}</math>? or <math>\frac{2}{5}</math>? | ||
| + | We see that <math>\frac{1}{3} = \frac{5}{15}</math>, and <math>\frac{2}{5} = \frac{6}{15}</math>, so obviously <math>\frac{2}{5}</math> is larger. | ||
==See Also== | ==See Also== | ||
[[1986 AJHSME Problems]] | [[1986 AJHSME Problems]] | ||
Revision as of 18:00, 20 January 2009
Problem
Which of the following numbers has the largest reciprocal?
Solution
For positive numbers, the larger the number, the smaller it's 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 larger.
