How many natural numbers up to 2001 are divisible by 3 or 4 but not by 5?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 801
Natural numbers divisible by 3 up to 2001 = 2001/3 = 667
Natural numbers divisible by 4 up to 2001 = 2001/4 = 500
Total numbers that are divisible by both 3 and 4 or divisible by 12
= 2001/12 = 166
Now we need to find the numbers that are not divisible by 5.
In case of 3 : taking LCM as 15
= 2001/15 = 133
In case of 4 : taking LCM = 20
= 2001/20 = 100
Now excluding the numbers that are occurring in both of them;
taking LCM 60
2001/60 = 33
Total number = 667 + 500 - 166 - 133 – 100 + 33 = 801