Last visit was: 28 Sep 2026, 10:11 It is currently 28 Sep 2026, 10:11
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
PREVIOUS TOPIC
NEXT TOPIC

|x^3|< 64

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 36203
Own Kudos [?]: 43449 [3]
Given Kudos: 27266
Send PM
|x^3|< 64 [#permalink] New post   08 Aug 2018, 16:12
1
Expert Reply
2
Bookmarks
00:00

Question Stats:

74% (01:05) correct 25% (00:53) wrong based on 221 sessions

Hide Show timer Statistics

\(|x^3|< 64\)

Quantity A
Quantity B
\(-x\)
\(-|x|\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Kudos for R.A.E
ShowHide Answer
Official Answer
D
User avatar
P
GreenlightTestPrep
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12842 [4]
Given Kudos: 136
Send PM

Top Member of the Month
Re: |x^3|< 64 [#permalink] New post   09 Aug 2018, 12:55
4
Carcass wrote:
\(|x^3|< 64\)

Quantity A
Quantity B
-x
-|x|




Let's test some possible values of x

CASE 1
Since |0³| < 64, x COULD equal 0
We get:
Quantity A: -0
Quantity B: -|0|

Evaluate to get:
Quantity A: 0
Quantity B: 0
In this case, the two quantities are EQUAL


CASE 2
Since |(-1)³| < 64, x COULD equal -1
We get:
Quantity A: -(-1)
Quantity B: -|-1|

Evaluate to get:
Quantity A: 1
Quantity B: -1
In this case, Quantity A IS GREATER

Answer: D

Cheers,
Brent
User avatar
B
kaziselim
Manager
Manager
Joined: 06 Jun 2018
Posts: 102
Own Kudos [?]: 128 [0]
Given Kudos: 4
Send PM
Re: |x^3|< 64 [#permalink] New post   09 Aug 2018, 15:47
1
Carcass wrote:
\(|x^3|< 64\)

Quantity A
Quantity B
-x
-|x|


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Kudos for R.A.E



30 sec approach :

It's impossible to determine the sign of a variable that keeps inside the absolute value sign. X could be positive or negative. U will get know definite value of x.

The best answer is D.
avatar
ajbgre
Retired Moderator
Joined: 31 Jul 2018
Posts: 32
Own Kudos [?]: 16 [0]
Given Kudos: 0
GPA: 3.07
Send PM
Re: |x^3|< 64 [#permalink] New post   10 Aug 2018, 03:38
I selected option B because -|x| = -x.

How is it the D? I still do not understand. Could anyone further explain both question and answer?

Thank you.
User avatar
P
GreenlightTestPrep
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12842 [0]
Given Kudos: 136
Send PM

Top Member of the Month
Re: |x^3|< 64 [#permalink] New post   10 Aug 2018, 05:07
1
ajbozdar wrote:
I selected option B because -|x| = -x.

How is it the D? I still do not understand. Could anyone further explain both question and answer?

Thank you.


It is not always the case that -|x| = -x

If x is a POSITIVE number, then -|x| = -x
For example, if x = 2, we get: -|2| = -2
Simplify to get: -2 = -2

However, if x is a NEGATIVE number, then it is NOT the case that -|x| = -x
For example, if x = -3, we get: -|-3| = -(-3)
Simplify to get: -3 = 3, which is NOT TRUE

Does that help?

Cheers,
Brent
avatar
ajbgre
Retired Moderator
Joined: 31 Jul 2018
Posts: 32
Own Kudos [?]: 16 [0]
Given Kudos: 0
GPA: 3.07
Send PM
Re: |x^3|< 64 [#permalink] New post   10 Aug 2018, 06:25
GreenlightTestPrep wrote:

However, if x is a NEGATIVE number, then it is NOT the case that -|x| = -x
For example, if x = -3, we get: -|-3| = -(-3)
Simplify to get: -3 = 3, which is NOT TRUE

Does that help?



I have learnt that any negative number under mod becomes positive.

If so, -|-3| = -(3) i.e. = -3

Did I learn the wrong concept of absolute value?
User avatar
P
GreenlightTestPrep
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12842 [0]
Given Kudos: 136
Send PM

Top Member of the Month
Re: |x^3|< 64 [#permalink] New post   10 Aug 2018, 08:13
1
ajbozdar wrote:
GreenlightTestPrep wrote:

However, if x is a NEGATIVE number, then it is NOT the case that -|x| = -x
For example, if x = -3, we get: -|-3| = -(-3)
Simplify to get: -3 = 3, which is NOT TRUE

Does that help?



I have learnt that any negative number under mod becomes positive.

If so, -|-3| = -(3) i.e. = -3

Did I learn the wrong concept of absolute value?



You learned the correct concept.
In my solution, you'l see that I also state that -|-3| = -(3) = -3

Cheers,
Brent
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 36203
Own Kudos [?]: 43449 [0]
Given Kudos: 27266
Send PM
Re: |x^3|< 64 [#permalink] New post   21 Oct 2018, 00:39
Expert Reply
Yes.

Regards
avatar
Hovsep
Manager
Manager
Joined: 23 Oct 2018
Posts: 57
Own Kudos [?]: 0 [0]
Given Kudos: 0
Send PM
Re: |x^3|< 64 [#permalink] New post   23 Oct 2018, 08:43
is it possible to have negative sign in absolut value
User avatar
S
aishumurali
Manager
Manager
Joined: 23 May 2021
Posts: 146
Own Kudos [?]: 47 [0]
Given Kudos: 23
Send PM
Re: |x^3|< 64 [#permalink] New post   29 Aug 2021, 20:24
I attempted this sum in a different way:

|x ^ 3| < 64 , hence x needs to be less than 4 . As x can be positive or negative, it can have the values : +1,-1 ; +2 , -2 ;
+3 , -3 .

Lets consider x = 3

QA : -3
QB : -3

a= b

Lets consider x = -3

QA : 3
QB : -3

a>b

hence Ans is D
User avatar
G
HarishKumar
GRE Instructor
Joined: 24 Dec 2018
Posts: 1151
Own Kudos [?]: 1543 [1]
Given Kudos: 28
Send PM
|x^3|< 64 [#permalink] New post   25 Jun 2023, 20:07
1
\(|x^3| < 64 \) \(\text { }\) implies the value of \(x\) could be positive or negative. So, we could write two equations

\(x^3 < 64 \) ......(1)

\((-x)^3 < 64\)......(2)

Now, Quantity B, \(-|x|\) will always be negative.

So, one of the two inequalities above, (1) or (2), has negative value for \(x\) and is equivalent to \(-|x|\), So both quantities are equal.

The other inequality will give \(x\) a positive value and hence it will be greater than Quantity B.

Therefore, the answer is D.
User avatar
bumpbot
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 6103
Own Kudos [?]: 87 [0]
Given Kudos: 0
Send PM
Re: |x^3|< 64 [#permalink] New post   17 Dec 2025, 01:20
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Prep Club for GRE Bot
gmatclubot
Re: |x^3|< 64 [#permalink]
17 Dec 2025, 01:20
Moderators:
adewale223
GRE Instructor
166 posts
bronaugust
GRE Forum Moderator
37 posts
VibhuAnurag
GRE Instructor
275 posts
Nsp10
Moderator
45 posts
tyrant100
GRE Forum Moderator
144 posts

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

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact | Advertise