Bunuel wrote:
The number of positive integers not greater than 100, which are not divisible by 2, 3 or 5 is
(A) 26
(B) 27
(C) 31
(D) 32
(E) 33
Are You Up For the Challenge: 700 Level Questions: 700 Level QuestionsLeast common multiple of 2,3,5 = 30
Multiple of 30 near 100 is 90.
From the 90 numbers, 90/2 = 45 are divisible by 2. Hence, the remaining 45 are NOT divisible by 2.
Of these 45 numbers, 45/3 = 15 are divisible by 3. Hence, the remaining 30 are NOT divisible by 3.
Of these 30 numbers, 30/5 = 6 are divisible by 5. Hence, the remaining 24 are NOT divisible by 5.
Thus, till 90, there are 24 numbers that are not divisible by 2, 3 or 5
From 91 to 100, there are 2 more numbers - 91 and 97
Thus, total numbers = 24 + 2 = 26
Answer A
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