2024 AMC 10A Problems/Problem 1
- 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]- 1 Problem
- 2 Solution 1 (Direct Computation)
- 3 Solution 2 (Distributive Property)
- 4 Solution 3 (Solution 1 but Distributive)
- 5 Solution 4 (Modular arithmetic, fast)
- 6 Solution 5 (Process of Elimination) (Not recommended)
- 7 Video Solution by Daily Dose of Math
- 8 Video Solution 1 by Power Solve
- 9 See also
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 (Solution 1 but Distributive)
Note that and , therefore the answer is .
~Tacos_are_yummy_1
Solution 4 (Modular arithmetic, fast)
Evaluating the given expression yields , so the answer is either (A) or (D). Evaluating yields . Because answer (D) is , that cannot be the answer, so we choose choice .
Solution 5 (Process of Elimination) (Not recommended)
We simply look at the units digit of the problem we have (or take mod ) 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
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.