The number of elements in the set n ∈ ℕ : 10 ≤ n ≤ 100 and 3 n - 3 is a multiple of 7 is _______.

Step-by-step solution

Given that n ∈ 10 , 100 and n ∈ N . Let us take the values of n = 1 , 2 , 3 , . . . and check whether 3 n - 3 is divisible by 7 or not. ⇒ 3 1 - 3 = 0 is divisible by 7 ⇒ 3 2 - 3 = 3 , 3 is not divisible by 7 ⇒ 3 6 = 7 k + 1 is not divisible by 7 ⇒ 3 7 = 7 α + 3 , ⇒ 3 7 - 3 = 7 α is divisible by 7 Similarly ⇒ 3 13 = 7 k + 1 7 α + 3 = 7 β + 3 ⇒ 3 13 - 3 = 7 β is divisible by 7 If we observe the pattern for n = 1 , 7 , 13 , 3 n - 3 is divis