Last visit was: 21 Nov 2024, 14:05 It is currently 21 Nov 2024, 14:05

Close

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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GRE score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Own Kudos [?]: 3621 [1]
Given Kudos: 1053
GPA: 3.39
Send PM
Verbal Expert
Joined: 18 Apr 2015
Posts: 30003
Own Kudos [?]: 36336 [1]
Given Kudos: 25927
Send PM
Retired Moderator
Joined: 09 Nov 2021
Status:GRE Tutor London and Online
Affiliations: Private GMAT/GRE Tutor London
Posts: 76
Own Kudos [?]: 86 [1]
Given Kudos: 6
Send PM
Intern
Intern
Joined: 01 Sep 2024
Posts: 6
Own Kudos [?]: 2 [0]
Given Kudos: 48
Send PM
Re: If |x| < x^2, which of the following must be true? [#permalink]
Carcass wrote:
Given: \(|x|<x^2\);

Reduce by \(|x|\): \(1<|x|\) (side note: we can safely do this as absolute value is non-negative and in this case we know it's not zero too, as if x would be zero inequality wouldn't hold true, so \(|x|>0\));

So we have that \(x<-1\) or \(x>1\).

I. \(x^2>1\) --> always true;

II. \(x>0\) --> may or may not be true;

III. \(x<-1\) --> may or may not be true.

Answer: A (I only).


Could you please explain the case for III part? below in the reply the case for third part has been explained but it takes x as 2 whereas x is supposed to be a negative number here
Verbal Expert
Joined: 18 Apr 2015
Posts: 30003
Own Kudos [?]: 36336 [0]
Given Kudos: 25927
Send PM
Re: If |x| < x^2, which of the following must be true? [#permalink]
Expert Reply
\(|x|<x^2\) is given as fact and then we asked to determine which of the following statements MUST be true.

\(|x|<x^2\) means that either \(x<-1\) or \(x>1\), \(x\) can be ANY value from these two ranges, (I think in your own solution you've reached this conclusion: when \(x<-1\) the graph of \(|x|\) is below (less than) the graph of \(x^2\) and

when \(x>\)1 again the graph of \(|x|\) is below the graph of \(x^2\)).

Now, III says \(x<-1\) this statement is not always true as \(x\) can be for example 3 and in this case \(x<-1\) doesn't hold true.

Hope it's clear.
Prep Club for GRE Bot
Re: If |x| < x^2, which of the following must be true? [#permalink]
Moderators:
GRE Instructor
84 posts
GRE Forum Moderator
37 posts
Moderator
1111 posts
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne