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