Difference between revisions of "2024 AMC 10A Problems/Problem 1"

Revision as of 02:07, 31 January 2025

The following problem is from both the 2024 AMC 10A #1 and 2024 AMC 12A #1, so both problems redirect to this page.

Solution 8 (Super Fast)

It's not hard to observe and express $9901$ into $99\cdot100+1$ , and $10101$ into $101\cdot100+1$ .

We then simplify the original expression into $(99\cdot100+1)\cdot101-99\cdot(101\cdot100+1)$ , which could then be simplified into $99\cdot100\cdot101+101-99\cdot100\cdot101-99$ , which we can get the answer of $101-99=\boxed{\textbf{(A) }2}$ .

~RULE101

Video Solution (⚡️ 1 min solve ⚡️)

https://youtu.be/RODYXdpipdc

~Education, the Study of Everything

Video Solution by Pi Academy

https://youtu.be/GPoTfGAf8bc?si=JYDhLVzfHUbXa3DW

Video Solution by FrankTutor

https://www.youtube.com/watch?v=ez095SvW5xI

Video Solution Daily Dose of Math

https://youtu.be/Z76bafQsqTc

~Thesmartgreekmathdude

Video Solution 1 by Power Solve

https://www.youtube.com/watch?v=j-37jvqzhrg

Video Solution by SpreadTheMathLove

https://www.youtube.com/watch?v=6SQ74nt3ynw

Video Solution by Math from my desk

https://www.youtube.com/watch?v=n_G6wi1ulzY

@@ Line 1: / Line 1: @@
 {{duplicate|[[2024 AMC 10A Problems/Problem 1|2024 AMC 10A #1]] and [[2024 AMC 12A Problems/Problem 1|2024 AMC 12A #1]]}}
-==Solution 7 (Cubes)==
-Let <math>x=100</math>. Then, we have
-\begin{align*}
-\cdot 9901=(x+1)\cdot (x^2-x+1)=x^3+1, \\
-\cdot 10101=(x-1)\cdot (x^2+x+1)=x^3-1.
-\end{align*}
-Then, the answer can be rewritten as <math>(x^3+1)-(x^3-1)= \boxed{\textbf{(A) }2}.</math>
-~erics118
 ==Solution 8 (Super Fast)==

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