Question

9⁷ –7⁹ is divisible by

• A. 6
• B. 24
• C. 64
• D. 72

Answer 1

Answer: (C)

64

Answer 2

We have 9² – 7⁹ = (1 + 8)⁷ –(1 –8)⁹

= (1 + ⁷C₁. 8¹ + ⁷C₂. 8² + …..+ ⁷C₇. 8⁷)

– (1 – ⁹C₁. 8¹ + ⁹C₂. 8² – ….– ⁹C₉.8⁹)

= 16 × 8 + 64 [(⁷C₂ + …..+⁷C₇. 8⁵) – (⁹C₂ – …. – ⁹C₉. 8⁷)]

= 64 (an integer)

Ž 9⁷ – 7⁹ is divisible by 64.

Hence (3) is correct answer.