2024 AMC 8 Problems/Problem 1

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

$222,222-22,222-2,222-222-22-2$ $\equiv 2-2-2-2-2-2$ $\equiv -8$ $\equiv 2$ So the solution is $(B)$ $2$

~nikhil ~ CXP

Solution 2

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

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2024 AMC 8 Problems/Problem 1

Problem

Solution 1

Solution 2