Difference between revisions of "2021 Fall AMC 12B Problems/Problem 7"
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<math>\textbf{(E)} \: x+y+z=1</math> | <math>\textbf{(E)} \: x+y+z=1</math> | ||
+ | |||
+ | ==Solution 1== | ||
+ | Plugging in every choice, we see that choice <math>\textbf{(D)}</math> works. | ||
+ | |||
+ | |||
+ | We have <math>y=x+1, z=x</math>, so | ||
+ | <cmath>x(x-y)+y(y-z)+z(z-x)=x(x-(x+1))+(x+1)((x+1)-x)+x(x-x)=x(-1)+(x+1)(1)=1.</cmath> | ||
+ | Our answer is <math>\textbf{(D)}</math>. | ||
+ | |||
+ | ~kingofpineapplz | ||
==Solution 1 (Bash) == | ==Solution 1 (Bash) == |
Revision as of 23:31, 23 November 2021
Problem
Which of the following conditions is sufficient to guarantee that integers ,
, and
satisfy the equation
and
and
and
and
Solution 1
Plugging in every choice, we see that choice works.
We have , so
Our answer is
.
~kingofpineapplz
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