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

[BTGModeratorVI]

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

[swerve]

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.

[Scott@TargetTestPrep]

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