The number of numbers from 1 to 200 which are divisible by neither 3 nor 7 is :
A. 115
B. 106
C. 103
D. less than 100
Answer: Option A
Solution(By Examveda Team)
The required number = Number of numbers, which are (divisible by 3 + divisible by 7 - divisible by 21)Number of number divisible by 3,
$$\eqalign{ & {\text{ = }} {\frac{{ {198 - 3} }}{3}} + 1 \cr & = 66 \cr} $$
Number of number divisible by 7
$$\eqalign{ & = {\frac{{ {196 - 7} }}{7}} + 1 \cr & = 28 \cr} $$
Number of number divisible by 21,
$$\eqalign{ & = {\frac{{ {189 - 21} }}{{21}}} + 1 \cr & = 9 \cr} $$
Thus, the divisible value
$$\eqalign{ & = {66 + 28 - 9} \cr & = 85 \cr} $$
Thus, number of numbers which are not divisible by 3 or 7
$$\eqalign{ & = {\text{ }}200{\text{ }} - {\text{ }}85 \cr & = {\text{ }}115 \cr} $$
Related Questions on Number System
Three numbers are in ratio 1 : 2 : 3 and HCF is 12. The numbers are:
A. 12, 24, 36
B. 11, 22, 33
C. 12, 24, 32
D. 5, 10, 15
Join The Discussion