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Question

Let A be the set of integers N such that
(i) 100 N500
(ii) N is even
(iii) N is divisible by either 2 or 3 or 4 but not by 7.
How many elements are there in set A?
  1. 170
  2. 173
  3. 171
  4. 172


Solution

The correct option is B 173
Number of even numbers from 100 to 500 (both included) = (500-100)/2 + 1 = 201.
This includes all the numbers that are even and divisible by 2, 3, and 4.
Now, number of even numbers divisible by 7 = (490-112)/14 + 1 = 27 + 1 = 28
Number of elements of A = 201 - 28 = 173

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