If \(m\) and \(n\) are negative integers, which of the following must be true?

[M7MBA]

If \(m\) and \(n\) are negative integers, which of the following must be true?

I. \(m + n < 0\)
II. \(mn > 0\)
III. \(mn > n\)

A. I only
B. II only
C. I and II
D. I and III
E. I, II, and III

Answer: E

Source: Princeton Review

[Scott@TargetTestPrep]

If \(m\) and \(n\) are negative integers, which of the following must be true?

I. \(m + n < 0\)
II. \(mn > 0\)
III. \(mn > n\)

A. I only
B. II only
C. I and II
D. I and III
E. I, II, and III

Answer: E

Source: Princeton Review

Solution:

Since the sum of the two negative numbers is negative, we see that I is true.

Similarly, since the product of two negative numbers is positive, we see that II is true.

Lastly, since the product of m and n, mn, is positive (because they are both negative), mn is greater than n (because n is a negative number). Therefore, III is true also.

Answer: E