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March 29, 2017

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You are given a positive integer such that when the integer is divided by 1995, the remainder is 75. What will the remainder be when the same positive integer is divided by 57?

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    Have you noticed that 57|1995? (reads 57 divides 1995) This means that 1995/57 leaves no remainder.

    This means that 1995/57 will also leave 75 as a remainder. Since 75 > 57, we will say that the remainder when the original integer is divided by 57 is actually 75-57=18.

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