kaarthikvs wrote:In a class of 100 students, numbered 1 to 100, all the even numbered students opt physics, all the students whose number is divisible by 3 opt Chemistry and all the students whose number is divisible by 5 opt Mathematics. How many students opt none of these subjects.
A) 3
B) 16
C) 26
D) 50
E) 74
We have asked to select the number of numbers that are not divisible by 2, 3, or 5
Numbers divisible by 2 ----> 100/2 ------> 50 All even numbers 2,4,......100.
Numbers divisible by 3 ----> (100/3)- even multiples of 3 ------> 17 the pattern of multiples of 3 is 3,6,9,12,....99 i.e. odd, even, odd, even,........odd so their will be 17 odd numbers and 16 even numbers. Here we will only consider odd multiples because even multiples we have already counted as 2's multiples.
Numbers divisible by 5 ----> only 7 cases -----> 5,25,35,55,65,85,95 ------> Rest all multiples are either of 2 or 3 or both and so not to be counted again.
Number of number divisible by 2,3,or 5 between 1 and 100 (both inclusive) = 50 + 17 + 7 = 74
Number of number not divisible by 2,3,or5 between 1 and 100 (both inclusive) = 26 ---Answer
Regards,
Abhijit
