Difference between revisions of "1960 AHSME Problems/Problem 19"
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==See Also== | ==See Also== | ||
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Revision as of 19:15, 10 May 2018
Problem
Consider equation 
where 
, and 
are positive integers, and equation 
,
where 
, and 
are positive integers. Then
Solution
Consider each option, one at a time.
For option A, let 
and 
. That means 
, so 
. That is not an integer, so option A is eliminated.
For option B, let 
and 
. That also means , so . That is also not an integer, so option B is eliminated.
For option C, let 
, 
, and 
. That means 
, so 
. Option C works.
For options D and E, let 
, 
, and 
. That means 
, so 
. Since the result is not an integer, options D and E are eliminated.
Thus, the answer is 
.
See Also
| 1960 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 18 |
Followed by Problem 20 | |
| 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 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 | ||
| All AHSME Problems and Solutions | ||
