Question

The number of integers between 1 to 250 which are divisible by 7 or 11?​

Answer 1

Answer:

How many integers between 1 to 200 are divisible by 7 or 11?

7,14,21,⋯,196are the integers between 1 to 200 which are divisible by 7.

It is an AP with first term a = 7, common difference 7 and last term 196

an=a+(n−1)d⟹196=7+(n−1)7⟹28=1+n−1⟹n=28

∴There are 28 numbers between 1 to 200 which are divisible by 7

11,22,33,⋯,198are the integers between 1 to 200 which are divisible by 11.

It is an AP with first term a = 11, common difference 11 and last term 198

an=a+(n−1)d⟹198=11+(n−1)11⟹18=1+n−1⟹n=18

∴There are 18 numbers between 1 to 200 which are divisible by 11

77 and 154 are the integers between 1 to 200 which are divisible by 11 as well as 7.

Answer 2

Answer:

The number of integers between 1 to 250 which are divisible by 7 or 11 are 54

Step-by-step explanation:

Number of integers between 1 to 250 which are divisible by 7, N(7) = 250/7 = 35

Number of integers between 1 to 250 which are divisible by 11, N(11) = 250/11 = 22

Number of integers between 1 to 250 which are divisible by 7 and 11 i.e. by 77, N(7 ∩ 11) = 3

Thus, Number of integers between 1 to 250 which are divisible by 7 or 11, N(7 ∪ 11) = N(7) + N(11) - N(7 ∩ 11)

               = 35 + 22 - 3

               = 54