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a – b > a + b
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Updated on: 18 Oct 2018, 09:19
Updated on: 18 Oct 2018, 09:19
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If \(a – b > a + b\), where a and b are integers, which of the following must be true?
Indicate all that apply.
A. \(a<0\)
B. \(b<0\)
C. \(ab<0\)
Indicate all that apply.
A. \(a<0\)
B. \(b<0\)
C. \(ab<0\)
Originally posted by ruposh6240 on 11 Oct 2018, 22:45.
Last edited by GreenlightTestPrep on 18 Oct 2018, 09:19, edited 2 times in total.
Last edited by GreenlightTestPrep on 18 Oct 2018, 09:19, edited 2 times in total.
Edited the entire question
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Re: a – b > a + b
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18 Oct 2018, 10:55
18 Oct 2018, 10:55
1
ruposh6240 wrote:
If \(a – b > a + b\), where a and b are integers, which of the following must be true?
Indicate all that apply.
A. \(a<0\)
B. \(b<0\)
C. \(ab<0\)
Indicate all that apply.
A. \(a<0\)
B. \(b<0\)
C. \(ab<0\)
GIVEN: a – b > a + b
Add b to both sides to get: a > a + 2b
Subtract a from both sides to get: 0 > 2b
Divide both sides by 2 to get: 0 > b
So, statement B is the only statement that MUST be true.
Answer: B
ASIDE: If you feel that A or C is also true, consider these counter-examples:
A. a < 0
Notice that a = 1 and b = -2 satisfies the given inequality a – b > a + b
So, the statement that a < 0 is definitely false.
B. ab < 0
Notice that a = -1 and b = -2 satisfies the given inequality a – b > a + b
In this case ab = (-1)(-2) = 2
So, the statement that ab < 0 is definitely false.
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Re: a – b > a + b
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07 Nov 2021, 09:00
07 Nov 2021, 09:00
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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