How many positive integers less than 100 are divisible by both 3 and 7 ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Any positive integer that is divisible by both 3 and 7 is divisible by their product, $3 \times 7=21$. That is, we are being asked to count the number of positive integers less than 100 that are multiples of 21.

These integers are: $21,42,63$, and 84 .

We note that the next multiple of 21 is $21 \times 5=105$, which is greater than 100 .

There are 4 positive integers less than 100 that are divisible by both 3 and 7 .

ANSWER: (C)