Multiple choice general knowledge math & puzzles

How many numbers are there between 0 and 1000 which on division by 2, 4, 6, 8 leave remainders 1, 3, 5, 7 respectively?

  1. 21

  2. 40

  3. 41

  4. 39

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The number N that leaves remainder 1 when divided by 2, 3 when divided by 4, 5 when divided by 6, and 7 when divided by 8 satisfies N+1 is divisible by 2, 4, 6, and 8. The LCM of 2,4,6,8 is 24. So N = 24k - 1. For N between 0 and 1000, k can be 1,2,...,42 (since 24*42-1=1007). Thus there are 41 numbers. Checking: 23, 47, 71, 95, ... up to 999.