On dividing a positive integer n by 9, we get 7 as a remainder. What will be the remainder if (3n -1) is divided by 9?
(a) 1 (b) 2 (c) 3 (d) 4
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On dividing a positive integer n by 9, we get 7 as a remainder. What will be the remainder if (3n -1) is divided by 9?
(a) 1 (b) 2 (c) 3 (d) 4
On dividing a positive integer n by 9, we get 7 as a remainder. What will be the remainder if (3n -1) is divided by 9?
(a) 1 (b) 2 (c) 3 (d) 4
(b) 2
Let q be the quotient.
It is given that:
Remainder = 7
On applying Euclid’s algorithm, i.e. dividing n by 9, we have
n = 9q + 7
⇒ 3n = 27q + 21
⇒ 3n – 1 = 27q + 20
⇒ 3n – 1 = 9 × 3q + 9 × 2 + 2
⇒ 3n – 1 = 9 × (3q + 2) + 2
So, when (3n-1) is divided by 9, we get the remainder 2.