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If |a + b| c < d, which of the following must be true? Indicate all
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12 Jan 2023, 07:59
12 Jan 2023, 07:59
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64% (01:33) correct
35% (01:12) wrong based on 14 sessions
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If \(|a + b| − c < d\), which of the following must be true?
Indicate all that apply.
A. \(a + b > 0\)
B. \(d > 0\) whenever \(c < 0\)
C. \(d + c > 0\)
Indicate all that apply.
A. \(a + b > 0\)
B. \(d > 0\) whenever \(c < 0\)
C. \(d + c > 0\)
Re: If |a + b| c < d, which of the following must be true? Indicate all
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10 Feb 2023, 15:32
10 Feb 2023, 15:32
Expert Reply
Usually in the inequality questions is better first try to figure out conceptually rather than pick up numbers.
It is faster and easier versus lengthy and cumbersome+
we do know that |a + b| is always positive
So if we do have \(|a + b| − c < d\) then \(|a + b| < d+c\)
A+b is positive so must be d+c as well. So we do know that C is definitely true
Id c is negative and a+b is always positive then a positive number minus a negative one is always positive, and because we do have a positive number < d, it follows that d must be positive as well
So B is also true
As for a, we do know ONLY that a+b is inside the absolute value so it must be positive. However, per se we DO NOT know the sigh of a and b have taken singularly. So a, we cannot say for sure if it is true or false
The answer is B and C
It is faster and easier versus lengthy and cumbersome+
we do know that |a + b| is always positive
So if we do have \(|a + b| − c < d\) then \(|a + b| < d+c\)
A+b is positive so must be d+c as well. So we do know that C is definitely true
Id c is negative and a+b is always positive then a positive number minus a negative one is always positive, and because we do have a positive number < d, it follows that d must be positive as well
So B is also true
As for a, we do know ONLY that a+b is inside the absolute value so it must be positive. However, per se we DO NOT know the sigh of a and b have taken singularly. So a, we cannot say for sure if it is true or false
The answer is B and C
Re: If |a + b| c < d, which of the following must be true? Indicate all
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10 Apr 2024, 08:53
10 Apr 2024, 08:53
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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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