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

Revision as of 15:48, 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

2024 AMC 8 (Problems • Answer Key • Resources)
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All AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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 ~ nikhil
 ~ CXP
+==See Also==
+{{AMC8 box|year=2024|before=First Problem|num-a=2}}
+{{MAA Notice}}

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

Revision as of 15:48, 25 January 2024

Contents

Problem

Solution 1

Solution 2

See Also