Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2021 Fall AMC 12B Problems/Problem 7"

(→‎Solution)
(Tag: Blanking)
Line 1: Line 1:
 +
==Solution 1 (Bash) ==
  
 +
Just plug in all these options one by one, and one sees that all but <math>D</math> fails to satisfy the equation.
 +
 +
For <math>D</math>, substitute <math>z=x</math> and <math>y=x+1</math>:
 +
 +
<math>LHS=x(x-(x+1))+(x+1)(x+1-x)+x(x-x)=(-x)+(x+1)=1=RHS</math>
 +
 +
Hence the answer is <math>\boxed{\textbf{(D)}}.</math>

Revision as of 21:27, 23 November 2021

Solution 1 (Bash)

Just plug in all these options one by one, and one sees that all but $D$ fails to satisfy the equation.

For $D$, substitute $z=x$ and $y=x+1$:

$LHS=x(x-(x+1))+(x+1)(x+1-x)+x(x-x)=(-x)+(x+1)=1=RHS$

Hence the answer is $\boxed{\textbf{(D)}}.$

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2021_Fall_AMC_12B_Problems/Problem_7&oldid=165780"