If $m$ and $n$ are negative integers, which of the following must be true? I. $m + n 0$ 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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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Thu Nov 19, 2020 8:24 am

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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

Source: Beat The GMAT — Problem Solving | Thu Nov 19, 2020 8:24 am

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: If $m$ and $n$ are negative integers, which of the following must be true?

by Scott@TargetTestPrep » Mon Nov 30, 2020 10:51 am

M7MBA wrote: ↑
Thu Nov 19, 2020 8:24 am
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

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