Question

Find the number of numbers between 200 and 300, both included, which are not divisible by 2,3,4 and 5.

• A. 27
• B. 26
• C. 25
• D. 28

Answer 1

The correct option is B 26

Use the principle of counting. Start with 101 numbers (i.e. all numbers between 200 and 300 both included) and subtract the number of numbers which are divisible by 2 (viz. $\left[\frac{(300-200)}{2}\right]+1=51$ numbers), the number of numbers which are divisible by 3 but not by 2 (Note: This would be given by the number of terms in the series 201, 207, ... 297. This series has 17 terms) and the number of numbers which are divisible by 5 but not by 2 and 3. (The numbers are 205. 215. 235, 245, 265, 275, 295. A total of 7 numbers) Thus, the required answer is given by 101 - 51 - 17 - 7 = 26. Option (b) is correct.