GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Oct 2019, 13:37

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

Is x^3 > 1? (1) x > -2 (2) 2x – (b – c) < c – (b – 2)

Author Message
TAGS:

Hide Tags

Intern
Joined: 19 Apr 2018
Posts: 1
Is x^3 > 1? (1) x > -2 (2) 2x – (b – c) < c – (b – 2)  [#permalink]

Show Tags

Updated on: 10 Aug 2018, 01:08
1
00:00

Difficulty:

35% (medium)

Question Stats:

91% (01:12) correct 9% (01:19) wrong based on 31 sessions

HideShow timer Statistics

Is x^3 > 1?

(1) x > -2

(2) 2x – (b – c) < c – (b – 2)

Originally posted by ankita1211 on 08 Aug 2018, 09:10.
Last edited by Bunuel on 10 Aug 2018, 01:08, edited 3 times in total.
Renamed the topic, edited the question and added the OA.
Senior Manager
Joined: 22 Feb 2018
Posts: 420
Re: Is x^3 > 1? (1) x > -2 (2) 2x – (b – c) < c – (b – 2)  [#permalink]

Show Tags

08 Aug 2018, 09:52
ankita1211 wrote:
Is x^3> 1?
(1) x > -2
(2) 2x – (b – c) < c – (b – 2)

OA:B
Rephrasing the question
Subtracting 1 from both sides, we get
$$x^3-1>0$$
$$(x-1)(x^2+x+1)>0$$ [Using $$a^3 - b^3 = (a - b)(a^2 + b^2 + ab)$$]
$$x^2+x+1$$ is always positive, as its lowest value will occurs $$x=-\frac{1}{2}$$ i.e at $$\frac{-b}{{2a}}$$ given expression is of form $$ax^2+bx+c$$
At $$x=-\frac{1}{2}$$;$$x^2+x+1= {(-\frac{1}{2})}^2 -\frac{1}{2}+1=\frac{3}{4}$$

Lowest value of $$x^2+x+1$$ is $$\frac{3}{4}$$, for all other values of $$x$$ , $$x^2+x+1$$ would be greater than $$\frac{3}{4}$$

Question reduces: Is $$(x-1)>0?$$ or Is $$x>1$$

Statement 1 :$$x > -2$$
$$x$$ can be$$-1$$
Is $$x>1$$ : No
$$x$$ can be $$2$$
Is $$x>1$$ : yes
Statement 1 alone is not sufficient

Statement 2: $$2x – (b – c) < c – (b – 2)$$
$$2x -b+c< c-b+2$$
Adding $$b-c$$ on both sides, we get $$2x<2$$ or $$x<1$$
Is $$x>1$$ : No always
Statement 2 alone is sufficient
_________________
Good, good Let the kudos flow through you
Retired Moderator
Joined: 27 Oct 2017
Posts: 1256
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: Is x^3 > 1? (1) x > -2 (2) 2x – (b – c) < c – (b – 2)  [#permalink]

Show Tags

08 Aug 2018, 12:05
2
1
This question is based on an important Concept
Attachment:

WhatsApp Image 2018-08-09 at 00.31.35.jpeg [ 111.39 KiB | Viewed 489 times ]

_________________
Re: Is x^3 > 1? (1) x > -2 (2) 2x – (b – c) < c – (b – 2)   [#permalink] 08 Aug 2018, 12:05
Display posts from previous: Sort by