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

It is currently 13 Oct 2019, 22:50

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

If 6/(x(x+1))>1, which of the following could the value of x?

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

Hide Tags

Find Similar Topics 
Manager
Manager
User avatar
Joined: 14 Oct 2014
Posts: 66
Location: United States
GMAT 1: 500 Q36 V23
If 6/(x(x+1))>1, which of the following could the value of x?  [#permalink]

Show Tags

New post 21 Dec 2014, 16:23
3
19
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

79% (01:46) correct 21% (01:52) wrong based on 437 sessions

HideShow timer Statistics

If \(\frac{6}{x(x+1)}>1\), which of the following could the value of x?

A. -3.5
B. -2.5
C. 2.5
D. 3.5
E. 4.5
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15240
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If 6/(x(x+1))>1, which of the following could the value of x?  [#permalink]

Show Tags

New post 21 Dec 2014, 19:11
1
Hi viktorija,

This question can be solved by TESTing THE ANSWERS. One (and only one) or those numbers could be a solution to the given inequality, so we could check them (just plug them in) until we find one that "fits" the given inequality.

There is a logical math shortcut here though that we can take advantage of:

We're told that 6/(product) > 1 so the denominator must be LESS than 6. That way 6/(less than 6) will be > 1. So we're really just looking for a product that's less than 6. Logically, we're probably looking for a value for X that's relatively close to 0, so let's check answers B and C....But don't do the math just yet...

Answer B: X = -2.5
Denominator = (-2.5)(-1.5)

Answer C: X = 2.5
Denominator = (2.5)(3.5)

Since the negative signs will cancel out in Answer B, you don't have to do the math to see that Answer B is smaller. Since there's only one answer that will "fit", it has to be B.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Director
Director
User avatar
Joined: 07 Aug 2011
Posts: 502
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
GMAT ToolKit User
Re: If 6/(x(x+1))>1, which of the following could the value of x?  [#permalink]

Show Tags

New post 10 Jan 2015, 02:19
If 6/(x(x+1))>1, which of the following could the value of x?

A.-3.5
B.-2.5
C.2.5
D.3.5
E.4.5

Given 6/(x(x+1))>1 i.e x(x+1) is +ive implies X is positive ;
since we are dealing with all positives
6/(x(x+1))>1 ---> (x+3)(x-2)<0
++++++(-3)----(2)++++++
so anything between -3 and 2 satisfies the inequality .
B. -2.5

Bunuel am i doing right ?
Manager
Manager
avatar
Joined: 02 May 2014
Posts: 91
Schools: ESADE '16, HKU'16, SMU '16
GMAT 1: 620 Q46 V30
GMAT ToolKit User
Re: If 6/(x(x+1))>1, which of the following could the value of x?  [#permalink]

Show Tags

New post 10 Jan 2015, 04:26
Lucky2783 wrote:
If 6/(x(x+1))>1, which of the following could the value of x?

A.-3.5
B.-2.5
C.2.5
D.3.5
E.4.5

Given 6/(x(x+1))>1 i.e x(x+1) is +ive implies X is positive ;
since we are dealing with all positives
6/(x(x+1))>1 ---> (x+3)(x-2)<0
++++++(-3)----(2)++++++
so anything between -3 and 2 satisfies the inequality .
B. -2.5

Bunuel am i doing right ?


Lucky2783 ,I don't think this derivation of yours is right: x(x+1) is +ive implies X is positive. Please check!
Senior Manager
Senior Manager
User avatar
Joined: 13 Jun 2013
Posts: 266
Re: If 6/(x(x+1))>1, which of the following could the value of x?  [#permalink]

Show Tags

New post 10 Jan 2015, 06:01
viktorija wrote:
If 6/(x(x+1))>1, which of the following could the value of x?

A.-3.5
B.-2.5
C.2.5
D.3.5
E.4.5


\(\frac{6}{x(x+1)} >1\)

let's analyze the denominator. x(x+1) = x^2+x. now x^2+x will always be positive except for numbers lying between -1 and 0. now if x lies between -1 and 0, then the fraction
\(\frac{6}{x(x+1)}\) will be negative. this violates our initial given condition that \(\frac{6}{x(x+1)} >1\). hence the expression x^2+x will always be positive.

now since expression x^2+x is positive, therefore we can cross multiply. Thus we have
x^2+x<6
x^2+x-6<0
(x+3)(x-2)<0

now for all values of x which are less than -3, (x+3)(x-2) will always be positive. similarly for all values of x , which are greater than 2, (x+3)(x-2) will always be positive.

hence our desired range is between -3 and 2. i.e. -3<x<2. now out of the given options, only option b lies inside this range. hence answer must be B
Director
Director
User avatar
Joined: 07 Aug 2011
Posts: 502
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
GMAT ToolKit User
Re: If 6/(x(x+1))>1, which of the following could the value of x?  [#permalink]

Show Tags

New post 10 Jan 2015, 06:46
sytabish wrote:
Lucky2783 wrote:
If 6/(x(x+1))>1, which of the following could the value of x?

A.-3.5
B.-2.5
C.2.5
D.3.5
E.4.5

Given 6/(x(x+1))>1 i.e x(x+1) is +ive implies X is positive ;
since we are dealing with all positives
6/(x(x+1))>1 ---> (x+3)(x-2)<0
++++++(-3)----(2)++++++
so anything between -3 and 2 satisfies the inequality .
B. -2.5

Bunuel am i doing right ?


Lucky2783 ,I don't think this derivation of yours is right: x(x+1) is +ive implies X is positive. Please check!


thanks .
actually we do not need know the sign of X here
Given 6/(x(x+1))>1 implies (x(x+1)) is a +ive quantity so we can simply multilply both sides of inequality by (x(x+1))
6 > (x(x+1))
6> x^2 + x
x^2+x-6 < 0
(x+3)(x-2)<0
++++++(-3)----(2)++++++
so anything between -3 and 2 satisfies the inequality .
B. -2.5
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15240
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If 6/(x(x+1))>1, which of the following could the value of x?  [#permalink]

Show Tags

New post 10 Jan 2015, 13:37
Hi styabish,

You have to be very careful with your assumptions in the Quant section. This specific Number Property WILL show up on Test Day....

(X)(X+1) = positive

This does NOT mean that X has to be positive.

X COULD be positive....

eg
X = 1
(1)(2) = 2

X COULD be NEGATIVE though...

eg
X = -2
(-2)(-1) = 2

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1751
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If 6/(x(x+1))>1, which of the following could the value of x?  [#permalink]

Show Tags

New post 12 Jan 2015, 21:56
\(\frac{6}{(x(x+1))} > 1\)

\(\frac{6}{x^2 + x} > 1\)

For x = -3.5

\(\frac{6}{12.25-3.5}\) >> This would be less than 1

For x = -2.5

\(\frac{6}{6.25-2.5}\) >> This would be greater than 1

Answer = B
_________________
Kindly press "+1 Kudos" to appreciate :)
Intern
Intern
avatar
Joined: 22 Mar 2015
Posts: 4
Re: If 6/(x(x+1))>1, which of the following could the value of x?  [#permalink]

Show Tags

New post 21 Aug 2015, 08:27
viktorija wrote:
If 6/(x(x+1))>1, which of the following could the value of x?

A.-3.5
B.-2.5
C.2.5
D.3.5
E.4.5



isn't this what you get after factorising
x<-3 or x<2
then how is -2.5 the answer? (since -2.5 is greater than -3)
Can someone help, please?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58335
Re: If 6/(x(x+1))>1, which of the following could the value of x?  [#permalink]

Show Tags

New post 21 Aug 2015, 08:36
aggarwalpooja wrote:
viktorija wrote:
If 6/(x(x+1))>1, which of the following could the value of x?

A.-3.5
B.-2.5
C.2.5
D.3.5
E.4.5



isn't this what you get after factorising
x<-3 or x<2
then how is -2.5 the answer? (since -2.5 is greater than -3)
Can someone help, please?


Let me ask you: what does x < -3 (x is less than -3) or x < 2 (x is less than 2) even mean?

As for the solution please see above.


_________________
CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2603
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Reviews Badge
Re: If 6/(x(x+1))>1, which of the following could the value of x?  [#permalink]

Show Tags

New post 21 Aug 2015, 08:41
2
1
aggarwalpooja wrote:
viktorija wrote:
If 6/(x(x+1))>1, which of the following could the value of x?

A.-3.5
B.-2.5
C.2.5
D.3.5
E.4.5



isn't this what you get after factorising
x<-3 or x<2
then how is -2.5 the answer? (since -2.5 is greater than -3)
Can someone help, please?


The most straightforward method for this type of question will be to use the values in the options and see which one gives you >1 . Only 1 option must satisfy this requirement.

Additionally, for algebraic solution, look below:

Given : \(\frac{6}{x(x+1)} > 1\) ----> \(\frac{6}{x(x+1)} - 1 > 0\) ---> \(\frac{6-x^2-x}{x(x+1)} > 0\) ----> \(\frac{-6+x^2+x}{x(x+1)} < 0\)

\(\frac{(x+3)(x-2)}{x(x+1)} < 0\) ----> -3<x<-1 or 0<x<2

Only -2.5 lies in this range.

Hope this helps.
Intern
Intern
avatar
Joined: 22 Mar 2015
Posts: 4
Re: If 6/(x(x+1))>1, which of the following could the value of x?  [#permalink]

Show Tags

New post Updated on: 27 Aug 2015, 02:19
Bunuel wrote:
aggarwalpooja wrote:
viktorija wrote:
If 6/(x(x+1))>1, which of the following could the value of x?

A.-3.5
B.-2.5
C.2.5
D.3.5
E.4.5



isn't this what you get after factorising
x<-3 or x<2
then how is -2.5 the answer? (since -2.5 is greater than -3)
Can someone help, please?


Let me ask you: what does x < -3 (x is less than -3) or x < 2 (x is less than 2) even mean?

As for the solution please see above.

This link sorted my worries! For anyone who struggled in the last bit after factorising refer this:
https://www.khanacademy.org/math/algebr ... equalities

Thanks Bunuel! Now I know why did you ask me what didx < -3 (x is less than -3) or x < 2 (x is less than 2) even mean?

Originally posted by aggarwalpooja on 21 Aug 2015, 08:58.
Last edited by aggarwalpooja on 27 Aug 2015, 02:19, edited 1 time in total.
Intern
Intern
avatar
Joined: 22 Mar 2015
Posts: 4
Re: If 6/(x(x+1))>1, which of the following could the value of x?  [#permalink]

Show Tags

New post 21 Aug 2015, 09:15
Engr2012 wrote:
aggarwalpooja wrote:
viktorija wrote:
If 6/(x(x+1))>1, which of the following could the value of x?

A.-3.5
B.-2.5
C.2.5
D.3.5
E.4.5



isn't this what you get after factorising
x<-3 or x<2
then how is -2.5 the answer? (since -2.5 is greater than -3)
Can someone help, please?


The most straightforward method for this type of question will be to use the values in the options and see which one gives you >1 . Only 1 option must satisfy this requirement.

Additionally, for algebraic solution, look below:

Given : \(\frac{6}{x(x+1)} > 1\) ----> \(\frac{6}{x(x+1)} - 1 > 0\) ---> \(\frac{6-x^2-x}{x(x+1)} > 0\) ----> \(\frac{-6+x^2+x}{x(x+1)} < 0\)

\(\frac{(x+3)(x-2)}{x(x+1)} < 0\) ----> -3<x<-1 or 0<x<2

Only -2.5 lies in this range.

Hope this helps.


Thanks Engr12, plugging in the value is guess the easiest!
Manager
Manager
User avatar
S
Joined: 25 Mar 2013
Posts: 226
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
GMAT ToolKit User Reviews Badge
Re: If 6/(x(x+1))>1, which of the following could the value of x?  [#permalink]

Show Tags

New post 02 Jan 2017, 13:43
1
\(\frac{6}{(x(x+1))} > 1\)

6 > x(x+1)
\(6 > x^{2} + x\)
Plug In options
B
_________________
I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you
VP
VP
User avatar
D
Joined: 09 Mar 2016
Posts: 1232
Re: If 6/(x(x+1))>1, which of the following could the value of x?  [#permalink]

Show Tags

New post 20 Feb 2018, 11:10
Lucky2783 wrote:
sytabish wrote:
Lucky2783 wrote:
If 6/(x(x+1))>1, which of the following could the value of x?

A.-3.5
B.-2.5
C.2.5
D.3.5
E.4.5

Given 6/(x(x+1))>1 i.e x(x+1) is +ive implies X is positive ;
since we are dealing with all positives
6/(x(x+1))>1 ---> (x+3)(x-2)<0
++++++(-3)----(2)++++++
so anything between -3 and 2 satisfies the inequality .
B. -2.5

Bunuel am i doing right ?


Lucky2783 ,I don't think this derivation of yours is right: x(x+1) is +ive implies X is positive. Please check!


thanks .
actually we do not need know the sign of X here
Given 6/(x(x+1))>1 implies (x(x+1)) is a +ive quantity so we can simply multilply both sides of inequality by (x(x+1))
6 > (x(x+1))
6> x^2 + x
x^2+x-6 < 0
(x+3)(x-2)<0
++++++(-3)----(2)++++++
so anything between -3 and 2 satisfies the inequality .
B. -2.5


hello there! :)
How did you manage to draw the line based on this (x+3)(x-2)<0 is there rule to transform it into line ? :?
thank you :)
Senior Manager
Senior Manager
User avatar
P
Joined: 10 Apr 2018
Posts: 266
Location: United States (NC)
Re: If 6/(x(x+1))>1, which of the following could the value of x?  [#permalink]

Show Tags

New post 13 Sep 2018, 16:24
1
Hi dave13,

Let me try to respond to your query.

If \(\frac{6}{x(x+1)}\)>1, which of the following could the value of x?

note x and (x+1) are two consecutive numbers, then their product is always positive . Why
if x is negative then (x+1) is also negative and their product is always positive
if x is positive then (x+1) is also positive and their product is always positive
But x cannot be -1 and 0 , because the exp will be undefined for these values.

So
we can write \(\frac{6}{x(x+1)}\)>1 as \(\frac{6}{x(x+1)}\)-1>0

So \(\frac{(6-x(x+1)}{x(x+1)}\)>0

\(\frac{(6-x^2-x)}{x(x+1)}\)>0

\(\frac{-((x+3)(x-2))}{x(x+1)}\)>0

When we multiply by -1 on both sides we change the sign of inequality.

\(\frac{((x+3)(x-2))}{x(x+1)}\)<0

Now if you draw the number line and have positive and negative regions this is how it would look

++++++++++++(-3)---------------------(-1)++++++++++++(0)--------------------(2)++++++++++

Now the region where the inequality holds is
-3<x<-1 and 0<x<2

Now options B, C, D are greater than 2 so discard.
Option A is less than -3 so discard
Option B lies between -3<x<-1 so this could be possible value of for which the inequality will hold.


Probus
_________________
Probus

~You Just Can't beat the person who never gives up~ Babe Ruth
SVP
SVP
User avatar
V
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1687
Location: India
Concentration: International Business, Operations
Schools: INSEAD Jan '19
GPA: 3.01
WE: Engineering (Real Estate)
Reviews Badge CAT Tests
Re: If 6/(x(x+1))>1, which of the following could the value of x?  [#permalink]

Show Tags

New post 14 Sep 2018, 06:09
viktorija wrote:
If 6/(x(x+1))>1, which of the following could the value of x?

A.-3.5
B.-2.5
C.2.5
D.3.5
E.4.5


\(\frac{6}{[x (x + 1)]}\)\(> 1\)

\(\frac{6}{[x^2 + x]}\) > 1

We know that \(x^2 + x\) can never be negative irrespective of the value of \("x"\), therefore

\(6 > x^2 + x\)

Or \(x^2 + x - 6 < 0\)

\((x + 3) (x - 2) < 0\)

\((x - 2) < 0\) or \((x + 3) > 0\)

\(x < 2\) or \(x > -3\)

\(-3 < x < 2\)

Answer : B = \(-2.5\)
_________________
"Do not watch clock; Do what it does. KEEP GOING."
GMAT Club Bot
Re: If 6/(x(x+1))>1, which of the following could the value of x?   [#permalink] 14 Sep 2018, 06:09
Display posts from previous: Sort by

If 6/(x(x+1))>1, which of the following could the value of x?

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





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