2021 Fall AMC 12B Problems/Problem 7
- The following problem is from both the 2021 Fall AMC 10B #12 and 2021 Fall AMC 12B #7, so both problems redirect to this page.
Problem
Which of the following conditions is sufficient to guarantee that integers , , and satisfy the equation
and
and
and
and
Solution 1 (Bash)
Just plug in all these options one by one, and one sees that all but fails to satisfy the equation.
For , substitute and :
Hence the answer is
~Wilhelm Z
Solution 2
Plugging in every choice, we see that choice works.
We have , so
Our answer is .
~kingofpineapplz