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

It is currently 16 Oct 2019, 10:02

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.

Close

Request Expert Reply

Confirm Cancel

Is x greater than 3?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
B
Joined: 21 Jan 2019
Posts: 5
Is x greater than 3?  [#permalink]

Show Tags

New post 24 Feb 2019, 00:15
2
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

63% (01:20) correct 37% (01:22) wrong based on 54 sessions

HideShow timer Statistics

Is x > 3?

1) x >0
2) \(\sqrt{x^{3}-9x+4}\)>2
Manager
Manager
User avatar
G
Joined: 10 Apr 2018
Posts: 223
Location: India
Concentration: Entrepreneurship, Strategy
GMAT 1: 680 Q48 V34
GPA: 3.3
Premium Member Reviews Badge CAT Tests
Is x greater than 3?  [#permalink]

Show Tags

New post Updated on: 10 Oct 2019, 02:37
1
1
Objective: To find if x>3

From statement 1) we know that x>0, but from this we can't say whether or not x>3. So option A and D can be eliminated.

From statement 2) we get:
x^3-9x+4>2^2
x^3-9x+4>4
=> x^3-9x>0
=> x(x+3)(x-3)>0, so from this we can't say whether x>3 or not as x>3 and -3<x<0 are both valid solutions, so option B and D can be eliminated.

Combining statement 1) and 2), we get:
x>0 and x>3 or -3<x<0
Thus, we can say that x>3, so option C is the correct option.

Originally posted by iamsiddharthkapoor on 24 Feb 2019, 00:43.
Last edited by iamsiddharthkapoor on 10 Oct 2019, 02:37, edited 6 times in total.
Manager
Manager
avatar
S
Joined: 13 Oct 2018
Posts: 85
Location: India
GPA: 3.1
WE: Information Technology (Computer Software)
Is x greater than 3?  [#permalink]

Show Tags

New post Updated on: 24 Feb 2019, 00:47
Answer is C .

1. x> 0 no sufficent
2. if we square both side ,

we get x^3-9x+4 > 4
=> x^3-9x>4
x(x^2 -9)>0
x(x-3)(x+3) >0

Not sufficent .

If we combine both,

we get x>0 , it means , x-3 should be greater than 0 or x >3

So answer is C . Both are sufficient.

Hit Kudos now ??

Posted from my mobile device
_________________
Ankit
GMAT is tough so I am ...
Giving Kudos is the best way to encourage and appreciate people

Originally posted by kumarankit01 on 24 Feb 2019, 00:46.
Last edited by kumarankit01 on 24 Feb 2019, 00:47, edited 1 time in total.
Director
Director
User avatar
V
Status: Manager
Joined: 27 Oct 2018
Posts: 673
Location: Egypt
Concentration: Strategy, International Business
GPA: 3.67
WE: Pharmaceuticals (Health Care)
GMAT ToolKit User
Re: Is x greater than 3?  [#permalink]

Show Tags

New post 24 Feb 2019, 00:46
statement 1: x >0
x can be 2 or 10 , so clearly insufficient

statement 2: \(\sqrt{x^{3}-9x+4}\) > \(2\)
\(x^{3}-9x+4\) > \(4\)
\(x^{3}-9x\) > \(0\)
\(x(x^{2}-9)\) > \(0\)
\(x(x-3)(x+3)\) > \(0\)
so we have two valid intervals: \(x\) > \(3\) and \(0\) > \(x\) > \(-3\) . since one of them is \(> 3\) and the other is \(< 3\), so insufficient

by combining 1 and 2:
knowing \(x\) > \(0\) excludes the interval \(0\) > \(x\) > \(-3\), so left with the other interval \(x\) > \(3\), so sufficient
_________________
Thanks for Kudos
Intern
Intern
avatar
B
Joined: 21 Jan 2019
Posts: 5
Re: Is x greater than 3?  [#permalink]

Show Tags

New post 24 Feb 2019, 01:28
Question for managing time: how did you all get -3<x<0 quickly enough? were you able to test values within the time limit or did you surmise from the shape of a cubic graph?
Director
Director
User avatar
V
Status: Manager
Joined: 27 Oct 2018
Posts: 673
Location: Egypt
Concentration: Strategy, International Business
GPA: 3.67
WE: Pharmaceuticals (Health Care)
GMAT ToolKit User
Is x greater than 3?  [#permalink]

Show Tags

New post 24 Feb 2019, 01:53
1
sfoo wrote:
Question for managing time: how did you all get -3<x<0 quickly enough? were you able to test values within the time limit or did you surmise from the shape of a cubic graph?

Hi sfoo . the answer is "by speed drawing"

follow these steps:
step 1 : find key points of the equation
in our case, the equation is \(x(x-3)(x+3)\) > \(0\)
so the points are 0,3,-3

step 2: draw them on a straight light in ascending order
so you will have : -----------------------(-3)------------(0)----------(3)-------------

step 3: draw a parabolic line "like an "S" (wavy line starting with the biggest number, starting from the positive side (because x has positive sign beside it))

step 4: since the inequality is asking for intervals > 0, so we take the intervals above the straight line.

note: beware of the inequalities whether it is > or >=

try plugging in different equations in this plot to get sense of how things work: http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJ4XjIiLCJjb2xvciI6IiMwMDAwMDAifSx7InR5cGUiOjEwMDB9XQ--
Attachments

Untitled.png
Untitled.png [ 3.01 KiB | Viewed 495 times ]


_________________
Thanks for Kudos
Manager
Manager
User avatar
G
Joined: 10 Apr 2018
Posts: 223
Location: India
Concentration: Entrepreneurship, Strategy
GMAT 1: 680 Q48 V34
GPA: 3.3
Premium Member Reviews Badge CAT Tests
Is x greater than 3?  [#permalink]

Show Tags

New post 24 Feb 2019, 02:15
1
sfoo wrote:
Question for managing time: how did you all get -3<x<0 quickly enough? were you able to test values within the time limit or did you surmise from the shape of a cubic graph?


Check out the below link to learn how to quickly find solutions for such inequalities:

https://gmatclub.com/forum/wavy-line-me ... 24319.html
GMAT Club Bot
Is x greater than 3?   [#permalink] 24 Feb 2019, 02:15
Display posts from previous: Sort by

Is x greater than 3?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





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