Difference between revisions of "2024 AMC 8 Problems/Problem 1"
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==Problem 1== | ==Problem 1== | ||
− | What is the ones digit of <cmath>222, | + | What is the ones digit of <cmath>222,23 |
+ | 2-22,222-2,222-222-22-2?</cmath> | ||
<math>\textbf{(A) } 0\qquad\textbf{(B) } 2\qquad\textbf{(C) } 4\qquad\textbf{(D) } 6\qquad\textbf{(E) } 8</math> | <math>\textbf{(A) } 0\qquad\textbf{(B) } 2\qquad\textbf{(C) } 4\qquad\textbf{(D) } 6\qquad\textbf{(E) } 8</math> | ||
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==Solution 1== | ==Solution 1== | ||
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Revision as of 11:00, 20 April 2024
Contents
[hide]Problem 1
What is the ones digit of
Solution 1
− We can rewrite the expression as
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We note that the units digit of the addition is because all the units digits of the five numbers are and , which has a units digit of .
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Now, we have something with a units digit of subtracted from . The units digit of this expression is obviously , and we get as our answer.
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Solution 2
222,222-22,222 = 200,000 200,000 - 2,222 = 197778 197778 - 222 = 197556 197556 - 22 = 197534 197534 - 2 = 1957532
So our answer is .
Solution 3
We only care about the unit's digits.
Thus, ends in , ends in , ends in , ends in , and ends in .
Solution 4
We just take the units digit of each and subtract, or you can do it this way by adding an extra ten to the first number (so we don't get a negative number): Thus, we get the answer
Video Solution 1 (Quick and Easy!)
~Education, the Study of Everything
Video Solution (easy to understand)
https://youtu.be/BaE00H2SHQM?si=O0O0g7qq9AbhQN9I&t=130
~Math-X
Video Solution by Interstigation
https://youtu.be/ktzijuZtDas&t=36
See Also
2024 AMC 8 (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 AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.