Last visit was: 29 Apr 2026, 23:37

It is currently 29 Apr 2026, 23:37

Toolkit

Practice Tests

Quantitative Questions

Problem Solving (PS)

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

Request Expert Reply

Confirm Cancel

Back to Forum

Create Topic

If x is positive, which of the following could be correct ordering of

1 2 3

ramiav

Joined: 31 Oct 2022

Last visit: 19 Jun 2025

Posts: 31

Own Kudos:

Given Kudos: 16

Location: Spain

Concentration: Entrepreneurship, Technology

Schools: MIT '27 (WL) HBS '27 Stanford '27 (I) Columbia '27 (D) Haas '27 (S)

GMAT Focus 1: 705 Q86 V85 DI84 Verified score

Schools: MIT '27 (WL) HBS '27 Stanford '27 (I) Columbia '27 (D) Haas '27 (S)

GMAT Focus 1: 705 Q86 V85 DI84 Verified score

Posts: 31

Kudos: 54

14 Mar 2024, 02:53

Kudos

Bookmarks

My answer for visual thinkers, similar to the Bunuel with the critical points

( I find useful to learn how to draw 1/x - with vertical and horizontal offsets - the same as known line equations and parabolas )

You can see the 4 different zones A,B, P, Q - sorry for the letters
the limits are (0,1) (1, something between 1 and 2)((something between 1 and 2, 2 )(2, inf)

Show Spoiler

Attachment:

GMAT-Club-Forum-167dfckl.png [ 267.01 KiB | Viewed 577 times ]

de1234

Joined: 04 Dec 2024

Last visit: 09 Feb 2026

Posts: 36

Own Kudos:

Given Kudos: 1

GMAT Focus 1: 685 Q83 V83 DI86 Verified score

GMAT Focus 2: 695 Q88 V82 DI83 Verified score

Products:

GMAT Focus 2: 695 Q88 V82 DI83 Verified score

Posts: 36

Kudos: 2

15 Jul 2025, 06:11

Kudos

Bookmarks

Vavali

If x is positive, which of the following could be correct ordering of \(\frac{1}{x}\), \(2x\), and \(x^2\)?

I. \(x^2 < 2x < \frac{1}{x}\)

II. \(x^2 < \frac{1}{x} < 2x\)

III. \(2x < x^2 < \frac{1}{x}\)

(A) none
(B) I only
(C) III only
(D) I and II
(E) I, II and III

Here, Since we are asked a possible ordering, we should check each equation for certain value. If none of the iterations are true for the equality, we can say that the equality is wrong and if even one is correct we will say that the equality is correct.

Here selecting numbers to test the equality is the tricky part.

let's say that we have the numbers 2x,1/x and x^2 to compare. obviously the equality will change depending on the value of x. Observe each individual equality and make a decision. ( i assumed 1/2,0.9,1.5,3)

wArrior902

Joined: 19 Jan 2023

Last visit: 28 Apr 2026

Posts: 21

Own Kudos:

Given Kudos: 47

Posts: 21

Kudos: 6

18 Aug 2025, 09:56

Kudos

Bookmarks

This is very easily solvable using graphs. Create graphs of y = x^2, 2x and 1/x.

Graph of 1/x would be close to infinite at x = 0 and a smooth curve which goes to 0 as x goes to infinite. Make sure to intersect y = 1/x and x^2 at x = 1 and y = 1/x and 2x at x = 1/sqrt(2). Now you can see option 1 and 2 are correct from graphs directly.

Dream009

Joined: 05 Nov 2024

Last visit: 13 Mar 2026

Posts: 276

Own Kudos:

Given Kudos: 60

Location: India

Concentration: Strategy, Leadership

Schools: NYU Stern ESSEC IIM

GMAT Focus 1: 615 Q82 V79 DI80 Verified score

GRE 1: Q30 V50 Verified score

GPA: 84

WE:General Management (Consulting)

Products:

Schools: NYU Stern ESSEC IIM

GMAT Focus 1: 615 Q82 V79 DI80 Verified score

GRE 1: Q30 V50 Verified score

Posts: 276

Kudos: 99

20 Dec 2025, 21:28

Kudos

Bookmarks

easy way alert x is positive and that's the biggest saving grace here.
Let me show for statement 2
x^2<1/x
=> x^3 < 1
=> x < 1
So x^# is b/w 0 & 1
Also 1< 2x^2
0.5 < x^2
So X^2 can be 0.9 and whatever is that square root multiple with that again and it will surely be less than 1
Bingo this is possible

Apply same to Statement 3
2x<x^2
2<x
Also
X^2 <1/x
x^3<1
=> x <1
X has to be greater than 2 but other side says x is less than 1 - not possible

Similarly solve 1 and you will get the ans

Rickooreoisb

Joined: 18 Jul 2025

Last visit: 05 Apr 2026

Posts: 157

Own Kudos:

Given Kudos: 575

Location: India

Concentration: Finance, Marketing

GPA: 9

WE:Investment Banking (Finance: Investment Banking)

Posts: 157

Kudos: 41

12 Jan 2026, 11:18

Kudos

Bookmarks

Whenever you are given such cases to such, universe of values are

-2, -1.1, -1, -0.9, -0.5, 0, 0.5, 0.9, 1, 1.1 and 2

Since here the value of x is positive, try only 0.5, 0.9, 1, 1.1 and 2 and for 0.5 use it in fraction form

Kinshook

Major Poster

Joined: 03 Jun 2019

Last visit: 29 Apr 2026

Posts: 5,990

Own Kudos:

5,864

Given Kudos: 163

Location: India

Schools: HBS '26 CBS '26 Wharton '26

GMAT 1: 690 Q50 V34 Verified score

WE:Engineering (Transportation)

Products:

Schools: HBS '26 CBS '26 Wharton '26

GMAT 1: 690 Q50 V34 Verified score

Posts: 5,990

Kudos: 5,864

13 Jan 2026, 03:49

Kudos

Bookmarks

If x is positive, which of the following could be correct ordering of \(\frac{1}{x}\), \(2x\), and \(x^2\)?

I. \(x^2 < 2x < \frac{1}{x}\)
x^2 - 2x < 0; x(x-2)<0; 0<x<2
2x - 1/x < 0; (2x^2 - 1)/x < 0; Since x>0; 2x^2 - 1< 0; x^2 < 1/2; \(x < 1/\sqrt{2}\)
For\( 0<x<\frac{1}{\sqrt{2}}\), Possible

II. \(x^2 < \frac{1}{x} < 2x\)
x^2 - 1/x < 0; (x^3 - 1)/x < 0; x^3 - 1 < 0; (x-1)(x^2 + x + 1) < 0; x < 1 since (x+1/2)^2 + 3/4 > 0
1/x - 2x < 0; (1 - 2x^2)/x < 0; x^2 > 1/2; \(x > \frac{1}{\sqrt{2}}\)
\(\frac{1}{\sqrt{2}} < x < 1\); Possible

III. \(2x < x^2 < \frac{1}{x}\)
2x - x^2 < 0; x(x-2) > 0; x > 2
x^2 - 1/x < 0
(x^3 -1)/x < 0; (x-1)(x^2 + x + 1) < 0; x < 1 since (x+1/2)^2 + 3/4 > 0
Not possible since x < 1 & x> 2 is not possible simultaneously

(A) none
(B) I only
(C) III only
(D) I and II
(E) I, II and III

IMO D

messi16

Joined: 13 Aug 2025

Last visit: 14 Apr 2026

Posts: 44

Own Kudos:

Given Kudos: 3

Posts: 44

Kudos: 4

01 Mar 2026, 17:57

Kudos

Bookmarks

Honestly, this one is just one where I recommend solving by trying different numbers. If you try 1, 2, 3, 4, etc. you will notice a pattern that is not one of the options. HOWEVER, if you use decimals (I used .5 and .75) you will notice that I and II are the correct answers, thus answer choice D.