Last visit was: 13 Jun 2024, 22:20 It is currently 13 Jun 2024, 22:20
Toolkit
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

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.

# If x^3 < 16x, which of the following CANNOT be true?

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 93696
Own Kudos [?]: 631582 [5]
Given Kudos: 82279
Intern
Joined: 17 Mar 2019
Posts: 9
Own Kudos [?]: 27 [7]
Given Kudos: 65
Location: Brazil
Concentration: Entrepreneurship, Finance
General Discussion
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6814
Own Kudos [?]: 30532 [1]
Given Kudos: 799
Manager
Joined: 11 Dec 2020
Posts: 123
Own Kudos [?]: 46 [1]
Given Kudos: 56
Location: United States (NY)
Concentration: Operations, Economics
Schools: Booth '26
GPA: 3.7
Re: If x^3 < 16x, which of the following CANNOT be true? [#permalink]
1
Kudos
Bunuel wrote:
If x^3 < 16x, which of the following CANNOT be true?

(A) |x| > 4

(B) x > −4

(C) x < −4

(D) x > 4

(E) x < 4

Posted from my mobile device
Attachments

A0E506C3-FAE5-4D7D-934C-2815F061A4A3.jpeg [ 1.33 MiB | Viewed 2737 times ]

Intern
Joined: 04 Oct 2023
Posts: 36
Own Kudos [?]: 125 [0]
Given Kudos: 245
Location: India
GMAT Focus 1:
615 Q83 V83 DI75
GPA: 3.3
If x^3 < 16x, which of the following CANNOT be true? [#permalink]
@Bunuel
­where am i going wrong?
$$\\ X^{3} < 16x\\ X^{3} - 16x < 0\\ x(X^{2} - 4) < 0\\ x(x +4)(x-4) < 0 ,$$ for this to hold true we know x has to be negative

using number line
+                       -                       +
------------(-4)-------------------4---------

so equation will hold true when -4 < x < 4

but arent C & D subset of |x|>4 ?
and i understand why x > 4 is the right answer but i dont understand whats wrong in my number line approach­
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6065
Own Kudos [?]: 4738 [0]
Given Kudos: 463
Location: India
GPA: 3.5
Re: If x^3 < 16x, which of the following CANNOT be true? [#permalink]

Bunuel wrote:
If x^3 < 16x, which of the following CANNOT be true?

(A) |x| > 4

(B) x > −4

(C) x < −4

(D) x > 4

(E) x < 4

$$­x^3 < 16x$$

Or, $$x^2 < 16$$

So, $$x <$$­ +$$4$$­, Thus in a number line the value must lie to the left of $$+4$$­
Attachment:

inequality-outputter.gif [ 1.58 KiB | Viewed 677 times ]
­ NOw check only (D) points to the right direction , hence mus be incorrect !!!
Re: If x^3 < 16x, which of the following CANNOT be true? [#permalink]
Moderator:
Math Expert
93696 posts