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.
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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)
