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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
If |x| > 3, which of the following must be true?
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17 Nov 2021, 03:20
17 Nov 2021, 03:20
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Expert Reply
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Question Stats:
44% (01:05) correct
55% (01:29) wrong based on 27 sessions
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If |x| > 3, which of the following must be true?
I. x > 3
II. x^2 > 9
III. |x - 1| > 2
A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
I. x > 3
II. x^2 > 9
III. |x - 1| > 2
A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
If |x| > 3, which of the following must be true?
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17 Nov 2021, 19:29
17 Nov 2021, 19:29
1
\(|x| = \pm x\)
\(+x > 3\) and \(-x > 3 \Rightarrow x < 3\)
So I is false since there exist negative values of \(x\)
\(|x|^2 = (\pm x)^2 = x^2\)
\(x > 9 \Rightarrow x^2 > 3^2 \Rightarrow x^2 > 9\)
So, II is true
\(|x-1| > 2 \Rightarrow x-1 > 2\) & \(-x+1 > 2\)
\(x -1+1 > 2+1\) & \(-x+1-1>2-1\)
\(x > 3\) & \(-x>1 \Rightarrow x<1\)
\(x < 2\) is not always true.
So, III is false
Hence, Answer is B
\(+x > 3\) and \(-x > 3 \Rightarrow x < 3\)
So I is false since there exist negative values of \(x\)
\(|x|^2 = (\pm x)^2 = x^2\)
\(x > 9 \Rightarrow x^2 > 3^2 \Rightarrow x^2 > 9\)
So, II is true
\(|x-1| > 2 \Rightarrow x-1 > 2\) & \(-x+1 > 2\)
\(x -1+1 > 2+1\) & \(-x+1-1>2-1\)
\(x > 3\) & \(-x>1 \Rightarrow x<1\)
\(x < 2\) is not always true.
So, III is false
Hence, Answer is B
Re: If |x| > 3, which of the following must be true?
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11 Jun 2024, 06:38
11 Jun 2024, 06:38
I am also getting B here, because if |x - 1| > 2, then x > 3 or x < -1. So x can be -2, and |x| > 3 will not hold.
So what is the right answer here, can anyone help?
So what is the right answer here, can anyone help?
