Art of Problem Solving
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

2025 AMC 8 Problems/Problem 6: Difference between revisions

← Older editNewer edit →
Aaditmehta (talk | contribs)
editor
75 edits
Kashikasethi (talk | contribs)
editor
38 edits
No edit summary
Line 19: Line 19:


Note that this is not very practical and it is very time-consuming.
Note that this is not very practical and it is very time-consuming.
==Video Solution by Cool Math Problems ==
https://youtu.be/BRnILzqVwHk?si=1KwyuFBUDqdMtC6t&t=2


== Video Solution 1 by SpreadTheMathLove ==
== Video Solution 1 by SpreadTheMathLove ==

Revision as of 00:03, 3 February 2025

Problem

Sekou writes the numbers $15, 16, 17, 18, 19.$ After he erases one of his numbers, the sum of the remaining four numbers is a multiple of $4.$ Which number did he erase?

$\textbf{(A)}\ 15\qquad \textbf{(B)}\ 16\qquad \textbf{(C)}\ 17\qquad \textbf{(D)}\ 18\qquad \textbf{(E)}\ 19$

Solution 1

The sum of all five numbers is $85$. Since $85$ is $1$ more than a multiple of $4$, the number subtracted must be $1$ more than a multiple of $4$. Thus, the answer is $\boxed{\textbf{(C)}~17}$. ~Gavin_Deng

Solution 2

The sum of the residues of these numbers modulo $4$ is $-1+0+1+2+3=5 \equiv 1 \pmod 4$. Hence, the number being subtracted must be congruent to $1$ modulo $4$. The only such answer is $\boxed{\textbf{(C)}~17}$. ~cxsmi

Solution 3

We try out every number using brute force and get $\boxed{\textbf{(C)}~17}$

Note that this is not very practical and it is very time-consuming.

Video Solution by Cool Math Problems

https://youtu.be/BRnILzqVwHk?si=1KwyuFBUDqdMtC6t&t=2

Video Solution 1 by SpreadTheMathLove

https://www.youtube.com/watch?v=jTTcscvcQmI

Video Solution (A Clever Explanation You’ll Get Instantly)

https://youtu.be/VP7g-s8akMY?si=eMjbNcrUSiSp30ND&t=324 ~hsnacademy

Video Solution 2 by Thinking Feet

https://youtu.be/PKMpTS6b988

Video Solution by Daily Dose of Math

https://youtu.be/nkpdskFVgdM

~Thesmartgreekmathdude

See Also

2025 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 5 		Followed by
Problem 7
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 AJHSME/AMC 8 Problems and Solutions

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: File missing

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2025_AMC_8_Problems/Problem_6&oldid=241867"