Multiple choice general knowledge math & puzzles

If x = (163 + 173 + 183 + 193), then x divided by 70 leaves a remainder of

  1. 0

  2. 1

  3. 69

  4. 35
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the sum of cubes formula or modular arithmetic: 16^3 + 17^3 + 18^3 + 19^3. 16+19=35 and 17+18=35. Since a^3+b^3 is divisible by a+b, the sum is divisible by 35. Also, the sum of four consecutive cubes is divisible by 4. Thus it is divisible by 70, leaving remainder 0.

Keep practicing — related questions