The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is

Step-by-step solution

Two-digit numbers of the form 7 λ + 2 are 16 ,   23 ,   30 , . . . ,   93 These number are forming an arithmetic progression with first term a = 16 , common difference d = 23 - 16 = 7 and last term l = 93 And, we know that the last term of an arithmetic progression is given by l = a + n - 1 d ⇒ 93 = 16 + n - 1 7 ⇒ 77 = n - 1 7 ⇒ n = 12 Two-digit numbers of the form 7 λ + 5 are 12 ,   19 ,   26 , . . . ,   96 Again, using the last term of A . P . , we get 96