Track / Stage 3 / 9 of 260 #9 of 2000

Problem 9

AMC 10/12, early questions

Number theory Difficulty 3.0 Find the answer

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

Your answer

Official solution

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.
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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.