2024 AMC 8

Complete problem set with solutions and individual problem pages

Problem 1 Easy

What is the unit digit of:

222{,}222-22{,}222-2{,}222-222-22-2?

  • A.

    0

  • B.

    2

  • C.

    4

  • D.

    8

  • E.

    10

Answer:B

Solution 1

We can rewrite the expression as 222,222-(22,222+2,222+222+22+2). We note that the units digit of 22,222+2,222+222+22+2 is 0 because all the units digits of the five numbers are 2 and 5\cdot2=10, which has a units digit of 0. Now, we have something with a units digit of 0 subtracted from 222,222, and so the units digit of this expression is \boxed{\textbf{(B) } 2}.

 

Solution 2

We only care about the units digits. Thus, 2-2 ends in 0, 0-2 after regrouping(10-2) ends in 8, 8-2 ends in 6, 6-2 ends in 4, and 4-2 ends in \boxed{\textbf{(B) } 2}.