How many numbers are there from 500 to 550 (including both) that are neither divisible by 3 nor by 11?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 30.
Numbers divisible by 3 up to 500 = 500/3 = 166
Numbers divisible by 11 upto 500 = 500/11 = 45
Numbers divisible by 33 upto 500 = 500/33 = 15
Numbers divisible by 3 up to 550 = 550/3 = 183
Numbers divisible by 11 upto 550 = 550/11 = 50
Numbers divisible by 33 upto 550 = 550/33 = 16
So, numbers divisible by 3 between 500 and 550 = 183 - 166 = 17
Numbers divisible by 11 between 500 - 550 = 50 - 45 = 5
Numbers divisible by 33 between 500 - 550 = 16 - 15 = 1
Total numbers from 500 to 550 = 50 + 1 = 51
So, the total number which are not divisible by 3, 11 = 51 - (17 + 5 - 1) = 51 - 17- 5 + 1 = 30