Difference between revisions of "2024 AMC 8 Problems/Problem 1"

Revision as of 15:51, 25 January 2024

Problem

What is the ones digit of $222,222-22,222-2,222-222-22-2?$ $\textbf{(A) } 0\qquad\textbf{(B) } 2\qquad\textbf{(C) } 4\qquad\textbf{(D) } 6\qquad\textbf{(E) } 8$

Solution 1

We can rewrite the expression as $222,222-(22,222+2,222+222+22+2)$ .

We note that the units digit of the addition is $0$ because all the units digits of the five numbers are $2$ and $5*2=10$ , which has a units digit of $0$ .

Now, we have something with a units digit of $0$ subtracted from $222,222$ . The units digit of this expression is obviously $2$ , and we get $\boxed{B}$ as our answer.

~ Dreamer1297

Solution 2

$222,222-22,222-2,222-222-22-2$ $= 200,000 - 2,222 - 222 - 22 - 2$ $= 197778 - 222 - 22 - 2$ $= 197556 - 22 - 2$ $= 197534 - 2$ $= 197532$ This means the ones digit is $\boxed{(B) \hspace{1 mm} 2}$ $\newline$ ~ nikhil ~ CXP

Video Solution 1 (easy to digest) by Power Solve

https://www.youtube.com/watch?v=HE7JjZQ6xCk

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.

@@ Line 25: / Line 25: @@
 ~ nikhil
 ~ CXP
+==Video Solution 1 (easy to digest) by Power Solve==
+https://www.youtube.com/watch?v=HE7JjZQ6xCk
 ==See Also==
 {{AMC8 box|year=2024|before=First Problem|num-a=2}}
 {{MAA Notice}}

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