Difference between revisions of "2024 AMC 10A Problems/Problem 1"
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== 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 | ||
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+ | == Video Solution by Daily Dose of Math == | ||
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+ | https://youtu.be/Z76bafQsqTc | ||
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+ | ~Thesmartgreekmathdude | ||
==See also== | ==See also== | ||
{{AMC10 box|year=2024|ab=A|before=First Problem|num-a=2}} | {{AMC10 box|year=2024|ab=A|before=First Problem|num-a=2}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 16:59, 8 November 2024
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
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.