AMC10 2015 B

AMC10 2015 B · Q10

AMC10 2015 B · Q10. It mainly tests Basic counting (rules of product/sum), Parity (odd/even).

What are the sign and units digit of the product of all the odd negative integers strictly greater than −2015?

所有严格大于 −2015 的奇负整数的乘积的符号和个位数是什么？

(A) It is a negative number ending with a 1. 负数，以1结尾。

(B) It is a positive number ending with a 1. 正数，以1结尾。

(D) It is a positive number ending with a 5. 正数，以5结尾。

(E) It is a negative number ending with a 0. 负数，以0结尾。

Answer

Correct choice: (C)

正确答案：（C）

Solution

There are 2014 negative integers strictly greater than -2015, and exactly half of them, or 1007, are odd. The product of an odd number of negative numbers is negative. Furthermore, because all factors are odd and some of them are multiples of 5, this product is an odd multiple of 5 and therefore has units digit 5.

严格大于 -2015 的负整数有 2014 个，其中正好一半，即 1007 个是奇数。奇数个负数的乘积为负。而且，因为所有因子都是奇数，其中一些是 5 的倍数，这个乘积是奇数倍的 5，因此个位数为 5。

Topics