Last visit was: 24 Apr 2026, 19:12 It is currently 24 Apr 2026, 19:12
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
User avatar
EncounterGMAT
User avatar
Joined: 10 Oct 2018
Last visit: 16 Oct 2019
Posts: 317
Own Kudos:
632
 [16]
Given Kudos: 185
Status:Whatever it takes!
GPA: 4
Posts: 317
Kudos: 632
 [16]
What is the range of values for z^2 given that (z^2 + 4)(z^2 - 2) < 0 19 Mar 2019, 05:17
Kudos
Add Kudos
16
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

65% (hard)

Question Stats:

53% (01:38) correct 47% (01:37) wrong based on 303 sessions

History

Date
Time
Result
Not Attempted Yet
What is the range of values for \(x^2\) given that \((x^2 + 4)(x^2 - 2) < 0\) ?


(A) \(-4 < x^2 < 2\)

(B) \(0 ≤ x^2 ≤ 2\)

(C) \(0 ≤ x^2 < 2\)

(D) \(0 < x^2 < 2\)

(E) \(-∞ < x < 2\)
ShowHide Answer
Official Answer
C
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 24 Apr 2026
Posts: 8,629
Own Kudos:
5,190
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GMAT Focus 2: 645 Q83 V82 DI81
GPA: 4
WE:Marketing (Energy)
Products:
GMAT Club Tests Forum Quiz
GMAT Focus 2: 645 Q83 V82 DI81
Posts: 8,629
Kudos: 5,190
What is the range of values for z^2 given that (z^2 + 4)(z^2 - 2) < 0 26 Mar 2019, 10:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
nm97
What is the range of values for \(x^2\) given that (\(x^2\)+4)(\(x^2\)-2)<0?
(A) -4 < \(x^2\) < 2
(B) 0 ≤ \(x^2\) ≤ 2
(C) 0 ≤ \(x^2\) < 2
(D) 0 < \(x^2\) < 2
(E) -∞ < x < 2
Show more

basic clue or trick to solve this question is to check our desired outcome using given options
we need is (\(x^2\)+4)(\(x^2\)-2)<0
so x has to be <2 ; it cannot be =2 as then (\(x^2\)+4)(\(x^2\)-2)<0 wont stand true
so negate options A,B
also
value x^2 cannot be-ve so option E negated
between option C & D
we can note that (\(x^2\)+4)(\(x^2\)-2)<0 will hold true when x^2=0 so IMO C is correct :cool:
avatar
Ish1996
avatar
Joined: 18 Jan 2019
Last visit: 27 Apr 2019
Posts: 19
Own Kudos:
2
Given Kudos: 35
Posts: 19
Kudos: 2
What is the range of values for z^2 given that (z^2 + 4)(z^2 - 2) < 0 26 Mar 2019, 23:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Archit3110
nm97
What is the range of values for \(x^2\) given that (\(x^2\)+4)(\(x^2\)-2)<0?
(A) -4 < \(x^2\) < 2
(B) 0 ≤ \(x^2\) ≤ 2
(C) 0 ≤ \(x^2\) < 2
(D) 0 < \(x^2\) < 2
(E) -∞ < x < 2

basic clue or trick to solve this question is to check our desired outcome using given options
we need is (\(x^2\)+4)(\(x^2\)-2)<0
so x has to be <2 ; it cannot be =2 as then (\(x^2\)+4)(\(x^2\)-2)<0 wont stand true
so negate options A,B
also
value x^2 cannot be-ve so option E negated
between option C & D
we can note that (\(x^2\)+4)(\(x^2\)-2)<0 will hold true when x^2=0 so IMO C is correct :cool:
Show more

can you explain why A is wrong? the values in this range satisfy the condition
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 24 Apr 2026
Posts: 8,629
Own Kudos:
5,190
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GMAT Focus 2: 645 Q83 V82 DI81
GPA: 4
WE:Marketing (Energy)
Products:
GMAT Club Tests Forum Quiz
GMAT Focus 2: 645 Q83 V82 DI81
Posts: 8,629
Kudos: 5,190
What is the range of values for z^2 given that (z^2 + 4)(z^2 - 2) < 0 26 Mar 2019, 23:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Ish1996
Archit3110
nm97
What is the range of values for \(x^2\) given that (\(x^2\)+4)(\(x^2\)-2)<0?
(A) -4 < \(x^2\) < 2
(B) 0 ≤ \(x^2\) ≤ 2
(C) 0 ≤ \(x^2\) < 2
(D) 0 < \(x^2\) < 2
(E) -∞ < x < 2

basic clue or trick to solve this question is to check our desired outcome using given options
we need is (\(x^2\)+4)(\(x^2\)-2)<0
so x has to be <2 ; it cannot be =2 as then (\(x^2\)+4)(\(x^2\)-2)<0 wont stand true
so negate options A,B
also
value x^2 cannot be-ve so option E negated
between option C & D
we can note that (\(x^2\)+4)(\(x^2\)-2)<0 will hold true when x^2=0 so IMO C is correct :cool:

can you explain why A is wrong? the values in this range satisfy the condition
Show more

the range option A does not satisfy the inequality...
see we need a range where we get values<0 ; so substitute different values and you shall get the answer.
avatar
Ish1996
avatar
Joined: 18 Jan 2019
Last visit: 27 Apr 2019
Posts: 19
Own Kudos:
2
Given Kudos: 35
Posts: 19
Kudos: 2
What is the range of values for z^2 given that (z^2 + 4)(z^2 - 2) < 0 26 Mar 2019, 23:50
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Ish1996
Archit3110
nm97
What is the range of values for \(x^2\) given that (\(x^2\)+4)(\(x^2\)-2)<0?
(A) -4 < \(x^2\) < 2
(B) 0 ≤ \(x^2\) ≤ 2
(C) 0 ≤ \(x^2\) < 2
(D) 0 < \(x^2\) < 2
(E) -∞ < x < 2

basic clue or trick to solve this question is to check our desired outcome using given options
we need is (\(x^2\)+4)(\(x^2\)-2)<0
so x has to be <2 ; it cannot be =2 as then (\(x^2\)+4)(\(x^2\)-2)<0 wont stand true
so negate options A,B
also
value x^2 cannot be-ve so option E negated
between option C & D
we can note that (\(x^2\)+4)(\(x^2\)-2)<0 will hold true when x^2=0 so IMO C is correct :cool:

can you explain why A is wrong? the values in this range satisfy the condition
Show more

Yeah you are right, I forgot about -2, thanks
avatar
vicky2019
avatar
Joined: 22 Sep 2018
Last visit: 18 Jan 2022
Posts: 22
Own Kudos:
32
Given Kudos: 65
Posts: 22
Kudos: 32
What is the range of values for z^2 given that (z^2 + 4)(z^2 - 2) < 0 30 Mar 2019, 10:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
nm97
What is the range of values for \(x^2\) given that (\(x^2\)+4)(\(x^2\)-2)<0?
(A) -4 < \(x^2\) < 2
(B) 0 ≤ \(x^2\) ≤ 2
(C) 0 ≤ \(x^2\) < 2
(D) 0 < \(x^2\) < 2
(E) -∞ < x < 2
Show more

In the equation (x^2 + 4)(x^2-2)<0..either (X^2 + 4) is negative or (x^2 - 2) is negative.

Clearly X^2+4 can never be negative. So X^2-2 is negative

X^2-2<0

x^2<2...only option C seems to agree with the equation
User avatar
BelalHossain046
User avatar
Joined: 11 Feb 2013
Last visit: 05 Apr 2023
Posts: 193
Own Kudos:
317
 [1]
Given Kudos: 60
Location: United States (TX)
Concentration: Finance
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GRE 1: Q165 V155
GPA: 3.05
WE:Analyst (Commercial Banking)
GMAT 2: 690 Q47 V38
GRE 1: Q165 V155
Posts: 193
Kudos: 317
 [1]
What is the range of values for z^2 given that (z^2 + 4)(z^2 - 2) < 0 30 Mar 2019, 11:33
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Given, (x^2+4)(x^2-2)<0

So, in between (x^2+4) and (x^2-2), one expression must be positive and the other one must be negative.

Since x^2=a square value=always Non negative, (x^2+4) must be positive and (x^2-2) must be negative.

Thus, (x^2-2)<0
Or, x^2<2
So, x^2 must be less then 2 and since x^2 is a square value, it must be NON negative.

X^2 must be 0 or greater than 0 but less than 2.

My answer is C.

Posted from my mobile device
avatar
HermesM11
avatar
Current Student
Joined: 09 Oct 2021
Last visit: 08 Jun 2022
Posts: 15
Own Kudos:
6
Given Kudos: 20
Location: El Salvador
Schools: Simon '24 (WA) Carlson (WL) Broad (A) BU (WL)
GMAT 1: 620 Q48 V27
GPA: 3.6
WE:Project Management (Other)
Schools: Simon '24 (WA) Carlson (WL) Broad (A) BU (WL)
GMAT 1: 620 Q48 V27
Posts: 15
Kudos: 6
What is the range of values for z^2 given that (z^2 + 4)(z^2 - 2) < 0 18 Oct 2021, 10:26
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Archit3110
nm97
What is the range of values for \(x^2\) given that (\(x^2\)+4)(\(x^2\)-2)<0?
(A) -4 < \(x^2\) < 2
(B) 0 ≤ \(x^2\) ≤ 2
(C) 0 ≤ \(x^2\) < 2
(D) 0 < \(x^2\) < 2
(E) -∞ < x < 2

basic clue or trick to solve this question is to check our desired outcome using given options
we need is (\(x^2\)+4)(\(x^2\)-2)<0
so x has to be <2 ; it cannot be =2 as then (\(x^2\)+4)(\(x^2\)-2)<0 wont stand true
so negate options A,B
also
value x^2 cannot be-ve so option E negated
between option C & D
we can note that (\(x^2\)+4)(\(x^2\)-2)<0 will hold true when x^2=0 so IMO C is correct :cool:
Show more

What about imaginary numbers? Do I need to forget about this concept on the GMAT? Because X could take values of 3i, 2i, etc. and therefore X^2 would be -3, -2, etc.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,818
Own Kudos:
811,087
 [1]
Given Kudos: 105,873
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: 109,818
Kudos: 811,087
 [1]
What is the range of values for z^2 given that (z^2 + 4)(z^2 - 2) < 0 18 Oct 2021, 10:32
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
HermesM11
Archit3110
nm97
What is the range of values for \(x^2\) given that (\(x^2\)+4)(\(x^2\)-2)<0?
(A) -4 < \(x^2\) < 2
(B) 0 ≤ \(x^2\) ≤ 2
(C) 0 ≤ \(x^2\) < 2
(D) 0 < \(x^2\) < 2
(E) -∞ < x < 2

basic clue or trick to solve this question is to check our desired outcome using given options
we need is (\(x^2\)+4)(\(x^2\)-2)<0
so x has to be <2 ; it cannot be =2 as then (\(x^2\)+4)(\(x^2\)-2)<0 wont stand true
so negate options A,B
also
value x^2 cannot be-ve so option E negated
between option C & D
we can note that (\(x^2\)+4)(\(x^2\)-2)<0 will hold true when x^2=0 so IMO C is correct :cool:

What about imaginary numbers? Do I need to forget about this concept on the GMAT? Because X could take values of 3i, 2i, etc. and therefore X^2 would be -3, -2, etc.
Show more

All numbers on the GMAT are real numbers by default.
User avatar
parasma
User avatar
Joined: 13 Mar 2021
Last visit: 03 Sep 2024
Posts: 59
Own Kudos:
40
 [1]
Given Kudos: 20
Posts: 59
Kudos: 40
 [1]
What is the range of values for z^2 given that (z^2 + 4)(z^2 - 2) < 0 18 Oct 2021, 22:06
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
EncounterGMAT
What is the range of values for \(x^2\) given that \((x^2 + 4)(x^2 - 2) < 0\) ?


(A) \(-4 < x^2 < 2\)

(B) \(0 ≤ x^2 ≤ 2\)

(C) \(0 ≤ x^2 < 2\)

(D) \(0 < x^2 < 2\)

(E) \(-∞ < x < 2\)
Show more


Let x^2= P

(P+4)(P-2)<0

So -4<P<2

as X^2 can not be negative so -4 is discarded.
0<=P<2
Because 0 is one of the solution included in the range of P.
So answer is 0≤ x^2 < 2
C.
User avatar
swim2109
User avatar
Joined: 09 Oct 2017
Last visit: 04 Apr 2024
Posts: 239
Own Kudos:
127
Given Kudos: 64
Location: Pakistan
Concentration: Finance, Strategy
Schools: Columbia CBS '24 (S) Fuqua '24 (WL) Marshall '24 (D) Sloan '24 (WA) Tepper '24 (WL) McCombs '24 Johnson '24 (A) Wharton '25
GMAT 1: 640 Q48 V31
GRE 1: Q169 V160
GPA: 2.83
Products:
My Reviews
Schools: Columbia CBS '24 (S) Fuqua '24 (WL) Marshall '24 (D) Sloan '24 (WA) Tepper '24 (WL) McCombs '24 Johnson '24 (A) Wharton '25
GMAT 1: 640 Q48 V31
GRE 1: Q169 V160
Posts: 239
Kudos: 127
What is the range of values for z^2 given that (z^2 + 4)(z^2 - 2) < 0 20 Oct 2021, 13:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
How to solve through wavy line method?
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,975
Own Kudos:
1,117
Posts: 38,975
Kudos: 1,117
What is the range of values for z^2 given that (z^2 + 4)(z^2 - 2) < 0 08 Feb 2025, 14:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109818 posts
Krunaal
Tuck School Moderator
853 posts