Question

The number 1992¹⁹⁹⁸ – 1955¹⁹⁹⁸ – 1938¹⁹⁹⁸ + 1901¹⁹⁹⁸ is divisible by k. Then value of k is-

• A. 666
• B. 3996
• C. 5994
• D. None of these

Answer 1

Answer: (A)

666

Answer 2

1992ⁿ – 1938ⁿ is divisible by (1992 – 1938) i.e., 54

1955ⁿ – 1901ⁿ is divisible by (1955 – 1901) i.e., 54

Ž The given number is divisible by 54.

1992ⁿ – 1955ⁿ is divisible by (1992 – 1955) i.e., 37

1938ⁿ – 1901ⁿ is divisible by (1938 – 1901) i.e., 37

The given number is divisible by 37

Ž Hence the given number is divisible by

54 × 37 = 1998

Ž divisible by 666 [since 666 × 3 = 1998].