In a set of integers from 140 to 200 inclusive, how many integers are divisible by 4 and 6? a)10 b)16 c)21 d)22 !

The answer to the question asked is 5.

The least common multiple of 4 and 6 is 12. In the range 140 to 200, there are

... floor(200/12) - ceiling(140/12) + 1 = 16 - 12 + 1 = 5

integers divisible by 12.

The list of answer choices suggests that the question is intended to be, "how many integers are divisible by 4 or 6?"

The number divisible by 4 is

... floor(200/4) - ceiling(140/4) + 1 = 50 - 35 + 1 = 16

The number divisible by 6 is

... floor(200/6) - ceiling(140/6) + 1 = 33 - 24 + 1 = 10

We know from the above that there are 5 values that are divisible by both 4 and 6, so will be counted twice if we simply add the above numbers. Hence the number of values divisible by 4 or 6 is

... 16 + 10 - 5 = 21 . . . . . corresponds to selection C)

step-by-step explanation: