Difference between revisions of "1975 AHSME Problems/Problem 7"
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==Problem== | ==Problem== | ||
| − | For which non-zero real numbers <math>x</math> is <math>\frac{|x-|x|\-|}{x}</math> a positive | + | For which non-zero real numbers <math>x</math> is <math>\frac{|x-|x|\-|}{x}</math> a positive integer? |
<math>\textbf{(A)}\ \text{for negative } x \text{ only} \qquad \\ | <math>\textbf{(A)}\ \text{for negative } x \text{ only} \qquad \\ | ||
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\textbf{(C)}\ \text{only for } x \text{ an even integer} \qquad \\ | \textbf{(C)}\ \text{only for } x \text{ an even integer} \qquad \\ | ||
\textbf{(D)}\ \text{for all non-zero real numbers } x \\ | \textbf{(D)}\ \text{for all non-zero real numbers } x \\ | ||
| − | \textbf{(E)}\ \text{for no non-zero real numbers } x </math> | + | \textbf{(E)}\ \text{for no non-zero real numbers } x </math> |
| − | |||
==Solution== | ==Solution== | ||
Latest revision as of 22:43, 6 October 2021
Problem
For which non-zero real numbers 
is 
a positive integer?
Solution
Solution by e_power_pi_times_i
Notice that if is negative, then the whole thing would amount to a negative number. Also notice that if is positive, then 
would be 
, hence the whole thing would amount to . Therefore, is positive 
.
See Also
| 1975 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
| 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. 
