2015 AMC 10B Problem 10

Problem 10 of 25EasierNumber Theory

What are the sign and units digit of the product of all the odd negative integers strictly greater than

-2015?

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Solution

There are

1007

odd numbers greater than

-2015.

Our product is of an odd number of negative numbers, so the result is negative. Also, we multiply by

-5

in there, so the product is a multiple of

5,

making it end in

5

0.

None of our factors are even, so the product can’t be even. Therefore, the product must end in

5.

Thus, the correct answer is C .