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?

Question

Mathematics

Karley

18 July, 14:19

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?

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Cody Giles · 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