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Q: What is the smallest number which is divisible by 7 but has a remainder of 1 when divided by 1 2 3 4 5 and 6?

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The answer is 8.

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It is not possible, because the number 4 is divisible by 2, and it's remainder is divisible by 2 also, so whatever number works for the "4 with a remainder of 2", will never work for "2 with a remainder of 1.

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