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.

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 $5$ 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 .

2015 AMC 10B Problem 10

Solution:

Problem 10 in Other Years