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

2024 DMC Mock 10 Problems/Problem 8

Revision as of 20:03, 16 September 2024 by Pateywatey (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Note the identity $a^2+b^2+c^2-ab-ba-ca=\frac{(a-b)^2+(b-c)^2+(c-a)^2}{2}$. Substituting in the values, we see that the expression is $\frac{3^2+4^2+7^2}{2}=\boxed{37}$. Alternatively, notice that the expression is 2$\pmod{5}$, so the answer must be $\boxed{B}$.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2024_DMC_Mock_10_Problems/Problem_8&oldid=227363"