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 "2025 AMC 8 Problems/Problem 4"

(→‎Solution 3 (Not the most practical))
(→‎Video Solution 1 by SpreadTheMathLove)
Line 25: Line 25:
 
~athreyay
 
~athreyay
  
−
== Video Solution 1 by SpreadTheMathLove ==
+
== Video Solution 1 (Detailed Explanation) 🚀⚡📊 ==
 +
 
 +
Youtube Link ⬇️
 +
https://youtu.be/rf5c9ulMA2I
 +
 
 +
~ ChillGuyDoesMath :)
 +
 
 +
== Video Solution by SpreadTheMathLove ==
  
 
https://www.youtube.com/watch?v=jTTcscvcQmI
 
https://www.youtube.com/watch?v=jTTcscvcQmI

Revision as of 19:13, 1 February 2025

Problem

Lucius is counting backward by $7$s. His first three numbers are $100$, $93$, and $86$. What is his $10$th number?

$\textbf{(A)}\ 30 \qquad \textbf{(B)}\ 37 \qquad \textbf{(C)}\ 42 \qquad \textbf{(D)}\ 44 \qquad \textbf{(E)}\ 47$

Solution 1

By the formula for the $n$th term of an arithmetic sequence, we get the answer $a+d(n-1)$ where $a=100, d=-7$ and $n=10$ which is equal to $100-7(10-1) = \boxed{\text{(B)\ 37}}$.

~Soupboy0

Solution 2

Since we want to find the $9$th number Lucius says after he says $100$, our answer is $100-(9 \cdot 7) = \boxed{\text{(B)\ 37}}$

~Sigmacuber

Solution 3 (Not the most practical)

Using brute force and counting backward by $7$s, we have $100, 93, 86, 79, 72, 65, 58, 51, 44, \boxed{\text{(B)\ 37}}$.

Note that this is not the most practical solution, and it is very time-consuming.

~athreyay

Video Solution 1 (Detailed Explanation) 🚀⚡📊

Youtube Link ⬇️ https://youtu.be/rf5c9ulMA2I

~ ChillGuyDoesMath :)

Video Solution by SpreadTheMathLove

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

Video Solution 2 by Daily Dose of Math

https://youtu.be/rjd0gigUsd0

~Thesmartgreekmathdude

Video Solution 3 by Thinking Feet

https://youtu.be/PKMpTS6b988

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

https://youtu.be/VP7g-s8akMY?si=K8Pxs_TQhlR2ntt9&t=211 ~hsnacademy

See Also

2025 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 3 		Followed by
Problem 5
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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2025_AMC_8_Problems/Problem_4&oldid=241677"