2022 · Q34
Consider the following statements :
- 1The sum of the cubes of three consecutive natural numbers is divisible by 9. 2. Every even power of every odd number (> 1) when divided by 8 gives 1 as remainder.
Which of the above statements is/are correct?
Elementary MathematicsNumber System
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
Cubes modulo 9 are only 0 and ±1; for every residue of n mod 3, n³+(n+1)³+(n+2)³ ≡ 0 (mod 9), so statement 1 holds. Every odd square is ≡ 1 (mod 8), and an even power is a square, so statement 2 holds. Hence the keyed option is C.