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

It is currently 20 Feb 2019, 07:37

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
Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT Prep Hour

     February 20, 2019

     February 20, 2019

     08:00 PM EST

     09:00 PM EST

    Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST
  • Online GMAT boot camp for FREE

     February 21, 2019

     February 21, 2019

     10:00 PM PST

     11:00 PM PST

    Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.

Is x between 0 and 1?

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

Hide Tags

 
Current Student
avatar
B
Joined: 28 Mar 2017
Posts: 30
Location: United Kingdom
GMAT 1: 710 Q48 V39
GPA: 2.7
Reviews Badge
Is x between 0 and 1?  [#permalink]

Show Tags

New post 05 Jun 2017, 13:17
1
1
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

72% (00:56) correct 28% (01:07) wrong based on 89 sessions

HideShow timer Statistics

Is \(x\) between 0 and 1?

1) \(x^{2}<x\)

2) \(x\) is positive

Can someone please explain the official answer? This is from the Veritas Prep Data Sufficiency book.
Current Student
avatar
B
Joined: 28 Mar 2017
Posts: 30
Location: United Kingdom
GMAT 1: 710 Q48 V39
GPA: 2.7
Reviews Badge
Re: Is x between 0 and 1?  [#permalink]

Show Tags

New post 05 Jun 2017, 13:39
1
What I don't get is why intuitively we know that x cannot be negative, since x^2 is always positive, but algebraically,

x^2<x
x^2-x<0
x(x-1)<0
x<0 or x<1

^here, x<0 or x<1. This shows x can be negative. Where am I going wrong?
CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3437
Location: Canada
Re: Is x between 0 and 1?  [#permalink]

Show Tags

New post 05 Jun 2017, 13:41
1
Top Contributor
bianalyst wrote:
Is \(x\) between 0 and 1?

1) \(x^{2}<x\)

2) \(x\) is positive



Target question: Is x between 0 and 1?

Statement 1: x² < x
Since we know that x² is POSITIVE, we can safely divide both sides of the inequality by x²
When we do this, we get: 1 < 1/x
If 1/x is greater than 1, we know that x must be POSITIVE (i.e., x > 0).
Since x is POSITIVE, we can safely multiply both sides of the inequality by x to get: x < 1
Combine the two inequalities to get: 0 < x < 1
In other words, x IS between 0 and 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x is positive
This doesn't tell us much.
It could be the case that x = 1/2, in which case, x IS between 0 and 1
Or it could be the case that x = 2, in which case, x is NOT between 0 and 1
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer:

RELATED VIDEO

_________________

Test confidently with gmatprepnow.com
Image

CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3437
Location: Canada
Re: Is x between 0 and 1?  [#permalink]

Show Tags

New post 05 Jun 2017, 13:46
1
1
Top Contributor
bianalyst wrote:
What I don't get is why intuitively we know that x cannot be negative, since x^2 is always positive, but algebraically,

1. x^2<x
2. x^2-x<0
3. x(x-1)<0
4. x<0 or x<1

^here, x<0 or x<1. This shows x can be negative. Where am I going wrong?


Everything is correct up to step #3.
Step #4 is incorrect.

You are taking a rule about EQUATIONS and applying it to INEQUALITIES (which we can't do)
IF it we had the EQUATION x(x-1) = 0, then we could conclude that x = 0 or x = 1

However, we can't make the same kind of conclusion when it comes to inequalities.
In fact, if we test a value like x = -1, we see that the step #3 inequality, x(x-1)<0, does not hold true. So, we can't conclude that x<0

Cheers,
Brent
_________________

Test confidently with gmatprepnow.com
Image

Current Student
avatar
B
Joined: 28 Mar 2017
Posts: 30
Location: United Kingdom
GMAT 1: 710 Q48 V39
GPA: 2.7
Reviews Badge
Re: Is x between 0 and 1?  [#permalink]

Show Tags

New post 05 Jun 2017, 13:54
Thanks - had no idea it only applied to equations. I'm trying to find a sure-fire algebraic approach to finding the range of values we can get from these types of inequalities questions; what approach would you recommend? I can see that you're determining the sign of x first and then dividing/multiplying to "solve" the inequality. Is this the general approach I should go for with these types of questions? Are there other ways to solve inequalities?
CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3437
Location: Canada
Re: Is x between 0 and 1?  [#permalink]

Show Tags

New post 05 Jun 2017, 13:57
Top Contributor
bianalyst wrote:
Is \(x\) between 0 and 1?

1) \(x^{2}<x\)

2) \(x\) is positive



Here's a even faster solution.

Target question: Is x between 0 and 1?

Statement 1: x² < x
For all values of x, x² will equal either zero or some positive number.
Since x is greater than x², we can be certain that x is positive.
Since x is POSITIVE, we can safely divide both sides of the inequality by x to get: x < 1
If x is positive AND x < 1, then we can be certain that x IS between 0 and 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x is positive
This doesn't tell us much.
It could be the case that x = 1/2, in which case, x IS between 0 and 1
Or it could be the case that x = 2, in which case, x is NOT between 0 and 1
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer:

RELATED VIDEO

_________________

Test confidently with gmatprepnow.com
Image

CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3437
Location: Canada
Re: Is x between 0 and 1?  [#permalink]

Show Tags

New post 05 Jun 2017, 14:00
1
Top Contributor
bianalyst wrote:
Thanks - had no idea it only applied to equations. I'm trying to find a sure-fire algebraic approach to finding the range of values we can get from these types of inequalities questions; what approach would you recommend? I can see that you're determining the sign of x first and then dividing/multiplying to "solve" the inequality. Is this the general approach I should go for with these types of questions? Are there other ways to solve inequalities?


This question can be treated as a quadratic inequality question, or it can be treated as a general inequality question.
This one is pretty straightforward, so I used the latter approach.
If you're given a more complex quadratic inequality, (e.g., x² - 5x - 6 > 0), then I suggest the quadratic inequality approach (see my video below).

RELATED VIDEO

_________________

Test confidently with gmatprepnow.com
Image

Current Student
avatar
B
Joined: 28 Mar 2017
Posts: 30
Location: United Kingdom
GMAT 1: 710 Q48 V39
GPA: 2.7
Reviews Badge
Re: Is x between 0 and 1?  [#permalink]

Show Tags

New post 05 Jun 2017, 14:22
GMATPrepNow wrote:
bianalyst wrote:
Thanks - had no idea it only applied to equations. I'm trying to find a sure-fire algebraic approach to finding the range of values we can get from these types of inequalities questions; what approach would you recommend? I can see that you're determining the sign of x first and then dividing/multiplying to "solve" the inequality. Is this the general approach I should go for with these types of questions? Are there other ways to solve inequalities?


This question can be treated as a quadratic inequality question, or it can be treated as a general inequality question.
This one is pretty straightforward, so I used the latter approach.
If you're given a more complex quadratic inequality, (e.g., x² - 5x - 6 > 0), then I suggest the quadratic inequality approach (see my video below).

RELATED VIDEO


Thanks, I actually found an easier solution that works for me - from my high school days I know what quadratic graphs look like, so I know in this case that this is a positive quadratic (x^2), and drawing out the parabola instantly tells me the range of x!
Current Student
avatar
B
Joined: 28 Mar 2017
Posts: 30
Location: United Kingdom
GMAT 1: 710 Q48 V39
GPA: 2.7
Reviews Badge
Re: Is x between 0 and 1?  [#permalink]

Show Tags

New post 05 Jun 2017, 14:28
Found Bunuel's graphical explanation here for anyone interested: https://gmatclub.com/forum/if-x-is-an-i ... ml#p731476
CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3437
Location: Canada
Re: Is x between 0 and 1?  [#permalink]

Show Tags

New post 05 Jun 2017, 15:20
Top Contributor
bianalyst wrote:
Thanks, I actually found an easier solution that works for me - from my high school days I know what quadratic graphs look like, so I know in this case that this is a positive quadratic (x^2), and drawing out the parabola instantly tells me the range of x!


I'm impressed that you remember how to graph parabolas from high school!! I'm sure most people can't make the same claim! :-D

Cheers,
Brent
_________________

Test confidently with gmatprepnow.com
Image

VP
VP
avatar
G
Joined: 09 Mar 2018
Posts: 1001
Location: India
Re: Is x between 0 and 1?  [#permalink]

Show Tags

New post 26 Jan 2019, 03:26
bianalyst wrote:
Is \(x\) between 0 and 1?

1) \(x^{2}<x\)

2) \(x\) is positive



Now x^2 will always be +ive, and the only region where

Statement 1 is true, is in between 0 and 1

Because higher the value of exponent lower is the value in the region of 0<x<1

Example 0.10 > 0.01,when x =0.1

Statement B doesn't tell us anything

A
_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

GMAT Club Bot
Re: Is x between 0 and 1?   [#permalink] 26 Jan 2019, 03:26
Display posts from previous: Sort by

Is x between 0 and 1?

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.