Difference between revisions of "2002 AMC 12P Problems/Problem 1"
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== Problem == | == Problem == | ||
| − | + | Which of the following numbers is a perfect square? | |
| − | <math> \ | + | <math> |
| + | \text{(A) }4^4 5^5 6^6 | ||
| + | \qquad | ||
| + | \text{(B) }4^4 5^6 6^5 | ||
| + | \qquad | ||
| + | \text{(C) }4^5 5^4 6^6 | ||
| + | \qquad | ||
| + | \text{(D) }4^6 5^4 6^5 | ||
| + | \qquad | ||
| + | \text{(E) }4^6 5^5 6^4 | ||
| + | </math> | ||
== Solution == | == Solution == | ||
Revision as of 23:54, 29 December 2023
Problem
Which of the following numbers is a perfect square?
Solution
If 
, then 
. Since 
, 
must be 
to some factor of 6. Thus, there are four (3, 9, 27, 729) possible values of 
.
See also
| 2000 AMC 12 (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 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
