Question

Let n₁, n₂, n₃ … be the increasing sequence of natural numbers each of which leaves remainder ' r ' when it is divided by (r +1) for r = 2, 3, 4, … 9. When n₂₀₀₈ is divided by 11, the remainder is –

• A. 4
• B. 7
• C. 5
• D. None of these

Answer 1

Answer: (C)

5

Answer 2

n₁ = LCM (2, 3, 4 … 9) – 1

n₂ = 2 × LCM (2, 3, 4, … 9) – 1

n₃ = 3 × LCM (2, 3, 4 … 9) – 1

n₂₀₀₈ = 2008 × LCM (2, 3, 4,… 9) – 1

= 2008 × 2520 – 1

= (229 × 11 + 1) (182 × 11 + 6) – 1

Remainder when n₂₀₀₈ is divided by 11 is 5.