How many positive integers less than 400 can be created using only the digits 1,2 or 3 , with repetition of digits allowed?
(A) 30
(B) 33
(C) 36
(D) 39
(E) 42
We must consider that the integers created could be one-digit, two-digit or three-digit integers. First, consider one-digit integers.

Since 1, 2 and 3 are the only digits that may be used, then there are only 3 one-digit positive integers less than 400, namely 1,2 and 3 .

Next, consider the number of two-digit integers that can be created.

Since digits may be repeated, the integers $11,12,13,21,22,23,31,32,33$ are the only possibilities.

Thus, there are 9 two-digit positive integers that can be created.

Instead of listing these 9 integers, another way to count how many there are is to consider that there are 3 choices for the first digit (either 1, 2 or 3 may be used) and also 3 choices for the second digit (since repetition of digits is allowed), so $3 \times 3=9$ possibilities.

Finally, we count the number of three-digit positive integers.

There are 3 choices for the first digit, 3 choices for the second digit and 3 choices for the third digit.

Thus, there are $3 \times 3 \times 3=27$ possible three-digit positive integers that can be created. (Note that all of these are less than 400 , since the largest of them is 333.)

In total, the number of positive integers less than 400 that can be created using only the digits 1,2 or 3 (with repetition allowed), is $3+9+27=39$.

ANSWER: (D)