GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2512
Given Kudos: 1060
GPA: 3.39
If |x| > 3, which of the following must be true?
[#permalink]
17 Nov 2021, 03:20
17 Nov 2021, 03:20
1
Expert Reply
00:00
Question Stats:
41% (01:05) correct
58% (01:30) wrong based on 29 sessions
Hide Show timer Statistics
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?
[#permalink]
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?
[#permalink]
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?
