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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If a – b > a + b, where a and b are integers, which of the following must be true?
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BTGModeratorVI
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Simplify the inequality:BTGModeratorVI wrote: ↑Fri Apr 03, 2020 9:33 amIf 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
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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Simplifying, we have:BTGModeratorVI wrote: ↑Fri Apr 03, 2020 9:33 amIf 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
- 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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