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This problem trains for: SAT-I, AMC-8, GMAT.

How many multiples of 3 or of 7 are there between -100 and 100?

There are:

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multiples of 3. There are

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multiples of 7. There are

equation

multiples of 7x3. There are

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multiples of 3 or 7 between 1 and 100.

There are

equation

multiples of 3 or 7 between -100 and 100 not counting 0. However, 0 is a multiple of any integer, therefore it must also be counted.

The solution is 87.