Difference between revisions of "2005 AMC 10A Problems/Problem 22"
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Since <math>4\cdot3=12</math> every <math>3</math>rd element of <math>S</math> will be a multiple of <math>12</math> | Since <math>4\cdot3=12</math> every <math>3</math>rd element of <math>S</math> will be a multiple of <math>12</math> | ||
| − | Therefore the answer is <math>\lfloor\frac{2005}{3}\rfloor=\boxed{\textbf{(D)} 668}</math> | + | Therefore the answer is <math>\left \lfloor\frac{2005}{3} \right \rfloor=\boxed{\textbf{(D)} 668}</math> |
~ LaTeX edits by dolphin7 | ~ LaTeX edits by dolphin7 | ||
Revision as of 13:55, 25 March 2020
Problem
Let 
be the set of the 
smallest positive multiples of 
, and let 
be the set of the smallest positive multiples of 
. How many elements are common to and ?
Solution
Since the least common multiple 
, the elements that are common to and must be multiples of 
.
Since 
and 
, several multiples of that are in won't be in , but all multiples of that are in will be in . So we just need to find the number of multiples of that are in .
Since 
every 
rd element of will be a multiple of
Therefore the answer is 
~ LaTeX edits by dolphin7
See Also
| 2005 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 21 |
Followed by Problem 23 | |
| 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 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
