If a – b > a + b, where a and b are integers, which of the following must be true? - The Beat The GMAT Forum

If a – b > a + b, where a and b are integers, which of the following must be true?

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pmFollowed by: 1 member

by BTGModeratorVI » Fri Apr 03, 2020 9:33 am

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If a – b > a + b, where a and b are integers, which of the following must be true?

I. a < 0
II. b < 0
III. ab < 0

A) I only
B) II only
C) I and II
D) I and III
E) II and III

Answer: B
Source: Manhattan prep

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Source: Beat The GMAT — Problem Solving | Fri Apr 03, 2020 9:33 am

swerve: Legendary Member; Posts: 2560; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

Re: If a – b > a + b, where a and b are integers, which of the following must be true?

by swerve » Fri Apr 03, 2020 2:41 pm

BTGModeratorVI wrote: ↑
Fri Apr 03, 2020 9:33 am
If a – b > a + b, where a and b are integers, which of the following must be true?

I. a < 0
II. b < 0
III. ab < 0

A) I only
B) II only
C) I and II
D) I and III
E) II and III

Answer: B
Source: Manhattan prep

Simplify the inequality:
a – b > a + b
b<0

We know for certain that II is true.

We don't have info about the value of a. Hence, I cannot be derived.

For III ab can be positive or negative depending on the value of a. Since we don't know about a, III cannot be inferred.

Hence, B is the answer.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8176; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: If a – b > a + b, where a and b are integers, which of the following must be true?

by Scott@TargetTestPrep » Sat Apr 25, 2020 1:36 pm

BTGModeratorVI wrote: ↑
Fri Apr 03, 2020 9:33 am
If a – b > a + b, where a and b are integers, which of the following must be true?

I. a < 0
II. b < 0
III. ab < 0

A) I only
B) II only
C) I and II
D) I and III
E) II and III

Answer: B
Source: Manhattan prep

Simplifying, we have:

- b > b

0 > 2b

0 > b

Since there are no restrictions on a, it can take any value. Thus, we see that a < 0 need not be true (since a can be positive or zero) and ab < 0 need not be true either (since a can be negative or zero). Thus, only statement II must be true.

Answer: B

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