Let S be the set of integers x such that: 1) 100 <= x <= 200 2) x is odd 3) x is divisible by 3 but not by 7. How many elements does S contain?

CAT 2000 Question Paper Question 135

Question 135

Let S be the set of integers x such that:

1) 100 <= x <= 200

2) x is odd

3) x is divisible by 3 but not by 7.

How many elements does S contain?

Solution

Number of multiples of 3 between 100 and 200 = 66 - 33 = 33
Number of odd multiples = 16
Number of odd multiples of 21 = 3 (105, 147, 189)
So, the required number = 13

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