Difference between revisions of "2024 AMC 10A Problems/Problem 1"
Line 30: | Line 30: | ||
== Solution 4 (Solution 1 but distrubutive) == | == Solution 4 (Solution 1 but distrubutive) == | ||
Note that <math>9901\cdot101=9901\cdot100+9901=9901=990100+9901=1000001</math> and <math>99\cdot10101=100\cdot10101-10101=1010100-10101=999999</math>, therefore the answer is <math>1000001-999999=\boxed{\text{(A) }2}</math> ~Tacos_are_yummy_1 | Note that <math>9901\cdot101=9901\cdot100+9901=9901=990100+9901=1000001</math> and <math>99\cdot10101=100\cdot10101-10101=1010100-10101=999999</math>, therefore the answer is <math>1000001-999999=\boxed{\text{(A) }2}</math> ~Tacos_are_yummy_1 | ||
− | |||
− | |||
− | |||
== Video Solution by Daily Dose of Math == | == Video Solution by Daily Dose of Math == | ||
Line 39: | Line 36: | ||
~Thesmartgreekmathdude | ~Thesmartgreekmathdude | ||
+ | |||
+ | == Video Solution 1 by Power Solve == | ||
+ | https://www.youtube.com/watch?v=j-37jvqzhrg | ||
==See also== | ==See also== |
Revision as of 21:41, 8 November 2024
- The following problem is from both the 2024 AMC 10A #1 and 2024 AMC 12A #1, so both problems redirect to this page.
Contents
[hide]Problem
What is the value of
Solution 1 (Direct Computation)
The likely fastest method will be direct computation. evaluates to and evaluates to . The difference is
Solution by juwushu.
Solution 2 (Distributive Property)
We have ~MRENTHUSIASM
Solution 3 (Process of Elimination) (Not recommended)
We simply look at the units digit of the problem we have(or take mod 10) Since the only answer with 2 in the units digit is or We can then continue if you are desperate to use guess and check or a actually valid method to find the answer is ~mathkiddus
Solution 4 (Solution 1 but distrubutive)
Note that and , therefore the answer is ~Tacos_are_yummy_1
Video Solution by Daily Dose of Math
~Thesmartgreekmathdude
Video Solution 1 by Power Solve
https://www.youtube.com/watch?v=j-37jvqzhrg
See also
2024 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
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 AMC 10 Problems and Solutions |
2024 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by First Problem |
Followed by Problem 2 |
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 AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.