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Q: How many numbers are there between 1 and 100 when divided by 24 gives a remainder 1?

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24, 30, 36, 42, 48 gives you five numbers between 20 and 50.

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23 is an odd number between 10 and 30 that gives a remainder of 2 when divided by 7.

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8.

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For the first seven numbers: 1 / 7 gives a remainder of 1 2 / 7 gives a remainder of 2 3 / 7 gives a remainder of 3 4 / 7 gives a remainder of 4 5 / 7 gives a remainder of 5 6 / 7 gives a remainder of 6 7 / 7 gives a remainder of 0 ... for a total of 21. After this, the pattern repeats. So, you need to find the closest multiple of seven that is less than 2010, see how many "cycles" you have there, multiply the number of cycles by 21, then separate calculate the remainder for the last few numbers.

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