Last visit was: 10 May 2026, 11:56 It is currently 10 May 2026, 11:56
Home
Messages
Tests
Schools
Events
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 
User avatar
Mck2023
User avatar
Joined: 23 Feb 2020
Last visit: 29 Apr 2026
Posts: 129
Own Kudos:
89
Given Kudos: 297
Location: Nepal
GMAT 1: 650 Q44 V35
GMAT 1: 650 Q44 V35
Posts: 129
Kudos: 89
Is x^5 > x^4? (1) x^3 > x (2) 1/x < x 07 Mar 2021, 20:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
HI Bunuel
Can you please help me understand this:

You reduced by x^4. i.e. x^4(x-1)>0, I guess!!
But I was not confident to do this because I had seen somewhere in 'finding the range of value of question', using wavy line method, where reducing directly like this got me wrong answer!! Can you please contrast between these two scenarios? Thank You!
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 10 May 2026
Posts: 110,237
Own Kudos:
814,074
Given Kudos: 106,164
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: 110,237
Kudos: 814,074
Is x^5 > x^4? (1) x^3 > x (2) 1/x < x 08 Mar 2021, 00:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Mck2023
HI Bunuel
Can you please help me understand this:

You reduced by x^4. i.e. x^4(x-1)>0, I guess!!
But I was not confident to do this because I had seen somewhere in 'finding the range of value of question', using wavy line method, where reducing directly like this got me wrong answer!! Can you please contrast between these two scenarios? Thank You!
Show more

We cannot divide an inequality by the variable if we don't know its sign. Here though x^4 cannot be negative, so we can divide and write x > 1.
User avatar
kavitaverma
User avatar
Joined: 26 May 2022
Last visit: 17 May 2024
Posts: 28
Own Kudos:
30
Given Kudos: 173
Location: India
Concentration: Technology, Other
GMAT 1: 730 Q50 V40
GMAT 1: 730 Q50 V40
Posts: 28
Kudos: 30
Is x^5 > x^4? (1) x^3 > x (2) 1/x < x 28 Apr 2023, 07:09
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Is x^5 > x^4?

Is \(x^5 > x^4\)? --> reduce by x^4: is \(x > 1\)?

(1) x^3 > −x --> \(x(x^2 + 1) > 0\). Since \(x^2 + 1\) is always positive, then the second multiple, x, must also be positive. So, this statement implies that x > 0. Not sufficient.

(2) 1/x < x --> multiply by x^2 (it has to be positive, so we can safely do that): \(x < x^3\) --> \(x(x^2 -1) > 0\) --> \((x + 1)x(x - 1) > 0\) --> \(-1 < x < 0\) or \(x > 1\). Not sufficient.

(1)+(2) Intersection of ranges from (1) and (2) is \(x > 1\). Sufficient.

Answer: C.
Show more


For option 2, \(-1 < x < 0\) or \(x > 1\).

isn't this range sufficient for the question to answer? IMO x^5 > x^4 for both the ranges. Or am I missing something here?

Bunuel @sayantanck please shed some light
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 10 May 2026
Posts: 110,237
Own Kudos:
814,074
 [1]
Given Kudos: 106,164
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: 110,237
Kudos: 814,074
 [1]
Is x^5 > x^4? (1) x^3 > x (2) 1/x < x 28 Apr 2023, 07:42
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
kavitaverma
Bunuel
Is x^5 > x^4?

Is \(x^5 > x^4\)? --> reduce by x^4: is \(x > 1\)?

(1) x^3 > −x --> \(x(x^2 + 1) > 0\). Since \(x^2 + 1\) is always positive, then the second multiple, x, must also be positive. So, this statement implies that x > 0. Not sufficient.

(2) 1/x < x --> multiply by x^2 (it has to be positive, so we can safely do that): \(x < x^3\) --> \(x(x^2 -1) > 0\) --> \((x + 1)x(x - 1) > 0\) --> \(-1 < x < 0\) or \(x > 1\). Not sufficient.

(1)+(2) Intersection of ranges from (1) and (2) is \(x > 1\). Sufficient.

Answer: C.


For option 2, \(-1 < x < 0\) or \(x > 1\).

isn't this range sufficient for the question to answer? IMO x^5 > x^4 for both the ranges. Or am I missing something here?

Bunuel @sayantanck please shed some light
Show more

The inequality x^5 > x^4 doesn't hold true when -1 < x < 0. For instance, when x = -1/2, x^5 becomes negative while x^4 is positive, making x^5 actually smaller than x^4, not larger.

I hope this helps.
User avatar
Vivek1707
User avatar
Joined: 22 May 2020
Last visit: 10 May 2026
Posts: 117
Own Kudos:
15
Given Kudos: 134
Products:
GMAT Club Tests
Posts: 117
Kudos: 15
Is x^5 > x^4? (1) x^3 > x (2) 1/x < x 17 Jan 2026, 04:23
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi Bunuel,

I have a question.

For the 2nd statement, In this solution when you have an expression such as

1/x < x

When you multiply by x^2 this becomes

x^2/x < x^3

From here when you reach x < x^3 arent you dividing the LHS by x and in that case since we dont know the sign of x shouldnt that be avoided as a step.

It may not have affected the solution in this question but going forward it can impact on another quesiton isnt it ?

Bunuel
Is x^5 > x^4?

Reduce by x^4 to rephrase the question:

Is \(x > 1\)?

(1) x^3 > −x

\(x(x^2 + 1) > 0\). Since \(x^2 + 1\) is always positive, then the second multiple, x, must also be positive. So, this statement implies that x > 0. Not sufficient.

(2) 1/x < x

Multiply by x^2 (it has to be positive, so we can safely do that):

\(x < x^3\);

\(x(x^2 -1) > 0\);

\((x + 1)x(x - 1) > 0\);

\(-1 < x < 0\) or \(x > 1\).

Not sufficient.

(1)+(2) Intersection of ranges from (1) and (2) is \(x > 1\). Sufficient.

Answer: C.
Show more
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 10 May 2026
Posts: 110,237
Own Kudos:
814,074
Given Kudos: 106,164
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: 110,237
Kudos: 814,074
Is x^5 > x^4? (1) x^3 > x (2) 1/x < x 18 Jan 2026, 01:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Vivek1707
Hi Bunuel,

I have a question.

For the 2nd statement, In this solution when you have an expression such as

1/x < x

When you multiply by x^2 this becomes

x^2/x < x^3

From here when you reach x < x^3 arent you dividing the LHS by x and in that case since we dont know the sign of x shouldnt that be avoided as a step.

It may not have affected the solution in this question but going forward it can impact on another quesiton isnt it ?


Show more
No issue here. We are not dividing by x. We multiply both sides by x^2, which is always positive, so the inequality direction is preserved. The step from x^2/x < x^3 to x < x^3 is just simplification on the left-hand side: x^2/x becomes x. We are not dividing both sides by x.
   1   2 
Moderators:
Bunuel
Math Expert
110237 posts
kingbucky
498 posts
Gmat860sanskar
241 posts