Question

A positive integer m when divided by 11 gives remainder 6. If 4m + 5 is divided by 11, the remainder is _________.

Answer 1

We know that,
Dividend = Divisor × Quotient + Remainder
⇒ m = 11 × q + 6 , where m is the dividend and q is the quotient
⇒ 4m = 11 × 4q + 24
⇒ 4m = 11 × 4q + 22 + 2
⇒ 4m = 11 × (4q + 2) + 2

Thus, if 4m is divided by 11, we get 2 as the remainder.

Therefore, If 4m + 5 is divided by 11, the remainder is 2 + 5 = 7.

Hence, If 4m + 5 is divided by 11, the remainder is 7 .