Difference between revisions of "1987 AHSME Problems/Problem 5"
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\textbf{(E)}\ 50</math> | \textbf{(E)}\ 50</math> | ||
| − | + | == Solution == | |
Note that <math>12.5\% = \frac{1}{8}</math>, <math>25\% = \frac{1}{4}</math>, and <math>50\% = \frac{1}{2}</math>. Thus, since the frequencies must be integers, <math>N</math> must be divisible by <math>2</math>, <math>4</math>, and <math>8</math> (so that <math>\frac{N}{8}</math> etc. are integers), or in other words, <math>N</math> is divisible by <math>8</math>. Thus the smallest possible value of <math>N</math> is the smallest positive multiple of <math>8</math>, which is <math>8</math> itself, or <math>\boxed{\text{B}}</math>. | Note that <math>12.5\% = \frac{1}{8}</math>, <math>25\% = \frac{1}{4}</math>, and <math>50\% = \frac{1}{2}</math>. Thus, since the frequencies must be integers, <math>N</math> must be divisible by <math>2</math>, <math>4</math>, and <math>8</math> (so that <math>\frac{N}{8}</math> etc. are integers), or in other words, <math>N</math> is divisible by <math>8</math>. Thus the smallest possible value of <math>N</math> is the smallest positive multiple of <math>8</math>, which is <math>8</math> itself, or <math>\boxed{\text{B}}</math>. | ||
Latest revision as of 11:25, 1 March 2018
Problem
A student recorded the exact percentage frequency distribution for a set of measurements, as shown below.
However, the student neglected to indicate 
, the total number of measurements. What is the smallest possible value of ?
![\[\begin{tabular}{c c}\text{measured value}&\text{percent frequency}\\ \hline 0 & 12.5\\ 1 & 0\\ 2 & 50\\ 3 & 25\\ 4 & 12.5\\ \hline\ & 100\\ \end{tabular}\]](http://latex.artofproblemsolving.com/6/9/6/6964fd0788b86327a9e769056847c55b958a1783.png)
Solution
Note that 
, 
, and 
. Thus, since the frequencies must be integers, must be divisible by 
, 
, and 
(so that 
etc. are integers), or in other words, is divisible by . Thus the smallest possible value of is the smallest positive multiple of , which is itself, or 
.
See also
| 1987 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 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 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
