Last visit was: 19 Nov 2025, 00:20 It is currently 19 Nov 2025, 00:20
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
GMAT 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 GMAT 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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
   1   2   3 
User avatar
ManavGidwani
User avatar
Joined: 15 Nov 2024
Last visit: 29 Sep 2025
Posts: 1
Posts: 1
Kudos: 0
If x/|x|<x which of the following must be true about x? 19 Sep 2025, 12:48
Kudos
Add Kudos
Bookmarks
Bookmark this Post
For eg if X is +0.5, which is which is X>-1 then so the output will be 1<0.5, hence the equation will not be true for all values of X>-1. Is my interpretation correct?
IanStewart
I'm pretty sure Durgesh has already explained his answer convincingly, but just in case, I'll present a different problem:

If x is positive, what must be true?

I) x > 10
II) x > -10
III) x > 0

Of course, III) says exactly 'x is positive', so III) must be true. But if x is positive, x is obviously larger than -10. II) must also be true. I) doesn't need to be true; x could be 4, or 7, for example.

The same situation applies with the question that began this thread. We know that either -1 < x < 0, or x > 1. What must be true? Well, "x > 1" does not need to be true. We know that x might be -0.5, for example. On the other hand, "x > -1" absolutely must be true: if x satisfies the inequality x/|x| < x, then x is certainly larger than -1. If we had been asked whether "x > -1,000,000" must be true, the answer would also be yes. The question did not ask "What is the solution set of "x/|x| < x"; nor did it ask "For which values of x is x/|x| < x true?".
Show more
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,379
Own Kudos:
778,147
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,379
Kudos: 778,147
If x/|x|<x which of the following must be true about x? 19 Sep 2025, 12:54
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ManavGidwani
For eg if X is +0.5, which is which is X>-1 then so the output will be 1<0.5, hence the equation will not be true for all values of X>-1. Is my interpretation correct?

Show more

No, your interpretation is not correct. This has already been explained several times in the thread, so please go through it carefully.

x cannot be 0.5, because the inequality holds true only for -1 < x < 0 and x > 1. For any x in these ranges, it is always true that x > -1.
   1   2   3 
Moderators:
Bunuel
Math Expert
105379 posts
Krunaal
Tuck School Moderator
805 posts