2015 AMC 10B Problem 10

Question

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

-2015?

It is a negative number ending with a

1.

It is a positive number ending with a

1.

It is a negative number ending with a

5.

It is a positive number ending with a

5.

It is a negative number ending with a

0.

Count how many odd negative factors there are

An odd product with a factor of

5

has units digit

5

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

or

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 .

Problem 10 in other years