2022 AMC 10B Problems/Problem 11
Problem
All the high schools in a large school district are involved in a fundraiser selling T-shirts. Which of the choices below is logically equivalent to the statement "No school bigger than Euclid HS sold more T-shirts than Euclid HS"?
All schools smaller than Euclid HS sold fewer T-shirts than Euclid HS.
No school that sold more T-shirts than Euclid HS is bigger than Euclid HS.
All schools bigger than Euclid HS sold fewer T-shirts than Euclid HS.
All schools that sold fewer T-shirts than Euclid HS are smaller than Euclid HS.
All schools smaller than Euclid HS sold more T-shirts than Euclid HS.
Solution
Let 
denote a school that is bigger than Euclid HS, and 
denote a school that sold more T-shirts than Euclid HS.
It follows that 
denotes a school that is not bigger than Euclid HS, and 
denotes a school that did not sell more T-shirts than Euclid HS.
Converting everything to conditional statements (if-then form), the given statement becomes
~MRENTHUSIASM
See Also
| 2022 AMC 10B (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 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
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