I am a number less than 3,000. When you divide me by 32, my remainder is 30. When you divide me by 58, my remainder is 44. What number am I?

n=32a+30=58b+44. Chinese remainder theorem whould have been useful, but you won't get it. So, you've got something more complicated in there... Well, you get numbers 30, 62, 94, 126, 158, 190, 222 etc for the first one and 44, 102, 160, 218 etc for the second one... I just can't do without that one! :)) The main idea is that you could calculate all numbers under 3000 in both conditions: the lists only share our number (supposedly :)) )

Answered by Anonymous | 2024-06-10

The answer is 3000 and I have it right

Answered by rohanpatel2211 | 2024-06-10

The number less than 3,000 that when divided by 32 leaves a remainder of 30 and when divided by 58 leaves a remainder of 44 is 270. This was found by setting up equations based on the conditions and testing integer values. The calculations confirmed that 270 satisfies both conditions.
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Answered by Anonymous | 2024-12-19