1985 AJHSME Problem 15

Problem

How many whole numbers between $100$ and $400$ contain the digit $2$ ?

$\text{(A)}\ 100 \qquad \text{(B)}\ 120 \qquad \text{(C)}\ 138 \qquad \text{(D)}\ 140 \qquad \text{(E)}\ 148$

Solution

There are $100$ numbers from 200 to 299 that have the number 2. In addition, there are 20 numbers that have a units digit of 2 and 20 numbers that have a tens digit of 2. However, we overcounted two numbers, 122 and 322.

Our final count is $100 + 20 + 20 - 2 = \boxed{\text{(C)}\ 138}$ numbers that contain the digit $2.$

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1985 AJHSME Problem 15

Problem

Solution