Question

I am a number less than 3000. When you divide me by 32, my remainder is 30. When you divide me by 58, my remainder 44. What number am I?

Answer 1

Let Q1 and Q2 be the quotients from dividing 32 and 58 respectively.Then 32 Q1 + 30 = 58 Q2 + 4432 Q1 = 58 Q2 + 1416 Q1 = 29 Q2 + 716 Q1 = (16 + 13)Q2 + 716 Q1 = 16 Q2 + 13 Q2 + 716(Q1 - Q2) = 13 Q2 + 7Because Q1 and Q2 are integers, we have to find Q2 whereby 13Q2 + 7 is divisible by 16.After some try-and-error, we get Q2 = 13. That is 13*13 + 7 = 176Therefore, Q1 - Q2 = 11 --> Q1 - 13 = 11 --> Q1 = 2432*24 + 30 = 58*13 + 44 = 798.I am 798