Difference between revisions of "2024 AMC 10A Problems/Problem 1"
Mathkiddus (talk | contribs) (→Solution 3 (Quickest Way)) |
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\end{align*}</cmath> | \end{align*}</cmath> | ||
~MRENTHUSIASM | ~MRENTHUSIASM | ||
− | == Solution 3 ( | + | == Solution 3 (A way to get rid of some answer choices(Not recommended on the actual competition) == |
We simply look at the units digit of the problem we have(or take mod 10) | We simply look at the units digit of the problem we have(or take mod 10) | ||
<cmath>9901\cdot101-99\cdot10101 \equiv 1\cdot1 - 9\cdot1 = 2 \mod{10}.</cmath> | <cmath>9901\cdot101-99\cdot10101 \equiv 1\cdot1 - 9\cdot1 = 2 \mod{10}.</cmath> | ||
− | Since the only answer with 2 in the units digit is <math>\boxed{\textbf{(A)}}</math> | + | Since the only answer with 2 in the units digit is <math>\textbf{(A)}</math> or <math>\textbf{(D)}</math> We can then continue if you are desperate to use guess and check or a actually valid method to find the answer is <math>\boxed{\textbf{(A)}}</math> |
~mathkiddus | ~mathkiddus | ||
Revision as of 15:30, 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 (A way to get rid of some answer choices(Not recommended on the actual competition)
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
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.