How many integers between 1 and 60 contain the digit 3 at least once?
(A) 6
(B) 10
(C) 14
(D) 15
(E) 20
Solution 1

There are 10 numbers (30 to 39 ) which have a tens digit of 3.

There are 6 numbers $(3,13,23,33,43,53)$ which have a units digit of 3.

In these two lists, there is one number counted twice, namely 33.

Therefore, the total number of different numbers in these two lists is $10+6-1=15$.

Solution 2

We list out the numbers in increasing order: $3,13,23,30,31,32,33,34,35,36,37,38,39,43$, 53. There are 15 of these numbers.