Difference between revisions of "2021 AIME II Problems/Problem 11"
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==Problem== | ==Problem== | ||
| − | + | A teacher was leading a class of four perfectly logical students. The teacher chose a set <math>S</math> of four integers and gave a different number in <math>S</math> to each student. Then the teacher announced to the class that the numbers in <math>S</math> were four consecutive two-digit positive integers, that some number in <math>S</math> was divisible by <math>6</math>, and a different number in <math>S</math> was divisible by <math>7</math>. The teacher then asked if any of the students could deduce what <math>S</math> is, but in unison, all of the students replied no. | |
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| + | However, upon hearing that all four students replied no, each student was able to determine the elements of <math>S</math>. Find the sum of all possible values of the greatest element of <math>S</math>. | ||
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==Solution== | ==Solution== | ||
We can't have a solution without a problem. | We can't have a solution without a problem. | ||
Revision as of 15:57, 22 March 2021
Problem
A teacher was leading a class of four perfectly logical students. The teacher chose a set 
of four integers and gave a different number in to each student. Then the teacher announced to the class that the numbers in were four consecutive two-digit positive integers, that some number in was divisible by 
, and a different number in was divisible by 
. The teacher then asked if any of the students could deduce what is, but in unison, all of the students replied no.
However, upon hearing that all four students replied no, each student was able to determine the elements of . Find the sum of all possible values of the greatest element of .
Solution
We can't have a solution without a problem.
See also
| 2021 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
