Multiple choice

Find the sum of the digits of the largest number of 2 digits, which leaves remainder 2 when divided by 3, 3 when divided by 4, and 5 when divided by 6.

  1. 13

  2. 8

  3. 14

  4. 5

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

We need the largest 2-digit number N where N≡2(mod 3), N≡3(mod 4), N≡5(mod 6). Numbers ≡5(mod 6) are: 95, 89, 83, 77... Checking conditions: 95÷3=32r2✓, 95÷4=23r3✓, 95÷6=15r5✓. Sum of digits of 95 = 9+5=14. Note: 98 fails as 98÷4=24r2.