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

It is currently 17 Oct 2018, 19:58

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 1?

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

Hide Tags

Intern
Intern
avatar
Joined: 28 Feb 2012
Posts: 24
Is x greater than 1?  [#permalink]

Show Tags

New post 06 Jun 2012, 21:20
1
5
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

65% (02:01) correct 35% (02:07) wrong based on 217 sessions

HideShow timer Statistics

Is x greater than 1?

(1) 1/x >−1

(2) 1/x^5 > 1/x^3
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49968
Re: Is x greater than 1?  [#permalink]

Show Tags

New post 07 Jun 2012, 16:53
3
3
sandal85 wrote:
Is x greater than 1?

(1) 1/x >−1

(2) 1/x^5 > 1/x^3


Question is \(x>1\)?

(1) \(\frac{1}{x}>- 1\) --> \(\frac{1+x}{x}>0\), two cases:

A. \(x>0\) and \(1+x>0\), \(x>-1\) --> \(x>0\);

B. \(x<0\) and \(1+x<0\), \(x<-1\) --> \(x<-1\).

We got that given inequality holds true in two ranges: \(x>0\) and \(x<-1\), thus \(x\) may or may not be greater than one. Not sufficient.

(2) \(\frac{1}{x^5}> \frac{1}{x^3}\) --> \(\frac{1-x^2}{x^5}>0\), two cases:

A. \(x>0\) (it's the same as \(x^5>0\)) and \(1-x^2>0\), \(-1<x<1\) --> \(0<x<1\);

B. \(x<0\) and \(1-x^2<0\), \(x<-1\) or \(x>1\) --> \(x<-1\);

We got that given inequality holds true in two ranges: \(0<x<1\) and \(x<-1\), ANY \(x\) from this ranges will be less than \(1\). So the answer to our original question is NO. Sufficient.

Answer: B.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
Intern
Intern
avatar
Joined: 24 May 2012
Posts: 1
Re: Is x greater than 1?  [#permalink]

Show Tags

New post 06 Jun 2012, 22:03
I go for E. Both statements are not sufficient to answer the question

Posted from my mobile device
Current Student
User avatar
B
Joined: 29 Mar 2012
Posts: 316
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
GMAT ToolKit User
Re: Is x greater than 1?  [#permalink]

Show Tags

New post 07 Jun 2012, 00:12
1
Hi,

Is x > 1?

Using option (1)
\(1/x > -1\)
or \(1/x + 1 >0\)
or \((1+x)/x > 0\)
=> \(x <-1\) or \(x >0\), Not sufficient.

Using option (2)
\(1/x^5 > 1/x^3\)
or \(1/x^5 - 1/x^3 >0\)
or \((1-x^2)/x^5 >0\)
or \((1-x)(1+x)/x^5>0\)
=> \(x <-1\) or\(0<x< 1\), and we have the answer to question "Is x > 1?" as NO

Hence, answer is (B)

Regards,
Intern
Intern
avatar
Joined: 20 May 2012
Posts: 18
Re: Is x greater than 1?  [#permalink]

Show Tags

New post 07 Jun 2012, 16:32
How did you factor the second statement like that?
1/x^5 > 1/x^3
or 1/x^5 - 1/x^3 >0
or (1-x^2)/x^5 >0
or (1-x)(1+x)/x^5>0
=> x <-1 or0<x< 1, and we have the answer to question "Is x > 1?" as N
Intern
Intern
avatar
Joined: 20 May 2012
Posts: 18
Re: Is x greater than 1?  [#permalink]

Show Tags

New post 07 Jun 2012, 16:57
Yes now I got it! Thanks! (i was simply cross multiplying for the statement 2 the first time!)
Intern
Intern
avatar
Joined: 07 Jan 2011
Posts: 19
Re: Is x greater than 1?  [#permalink]

Show Tags

New post 07 Jun 2012, 20:18
Bunuel
Sorry for asking this again, but I have been trying to do these type of sums only and not getting anywhere.

How can we have these 2 cases for an equation like (1+x)/x>0.

In the post out here it is mentioned is-x-between-0-and-1-1-x-2-is-less-than-x-2-x-3-is-104280.html#p1094206 that the signs should be different i.e. one should be > and the other lesser <. Now in this sum both the cases have the same sign. I did not get this.

The other thing also which I would like to ask is once we have an equation like this (1+x)/x >0 can we automatically write the 2 cases as (1+x) > 0 and x>0 and the other in opposite sign. Is this by rule.

It would be helpful if you could point me to some reading material on these type of sums where we get 2 cases for the root of the equation.

Thanks in advance.

Rahul Goel
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49968
Re: Is x greater than 1?  [#permalink]

Show Tags

New post 08 Jun 2012, 03:32
rggoel9 wrote:
Bunuel
Sorry for asking this again, but I have been trying to do these type of sums only and not getting anywhere.

How can we have these 2 cases for an equation like (1+x)/x>0.

In the post out here it is mentioned is-x-between-0-and-1-1-x-2-is-less-than-x-2-x-3-is-104280.html#p1094206 that the signs should be different i.e. one should be > and the other lesser <. Now in this sum both the cases have the same sign. I did not get this.

The other thing also which I would like to ask is once we have an equation like this (1+x)/x >0 can we automatically write the 2 cases as (1+x) > 0 and x>0 and the other in opposite sign. Is this by rule.

It would be helpful if you could point me to some reading material on these type of sums where we get 2 cases for the root of the equation.

Thanks in advance.

Rahul Goel


It's very basic:
ab>0 means that a and b must have the same sign;
ab<0 means that a and b must have the opposite signs.

Solving inequalities:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
everything-is-less-than-zero-108884.html?hilit=extreme#p868863
xy-plane-71492.html?hilit=solving%20quadratic#p841486

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 26 Dec 2011
Posts: 93
Re: Is x greater than 1?  [#permalink]

Show Tags

New post 14 Jun 2012, 07:11
By looking at condition 2, I think this condition is only feasible if x<0, for x>0 it will never be true, for example, x=2; thus from condition 2, we get x<0, thus the question whether x>1 is answered .. NO.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49968
Re: Is x greater than 1?  [#permalink]

Show Tags

New post 14 Jun 2012, 07:18
pavanpuneet wrote:
By looking at condition 2, I think this condition is only feasible if x<0, for x>0 it will never be true, for example, x=2; thus from condition 2, we get x<0, thus the question whether x>1 is answered .. NO.


That's not correct.

\(\frac{1}{x^5}> \frac{1}{x^3}\) holds true for \(0<x<1\) and \(x<-1\).

Check this:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
everything-is-less-than-zero-108884.html?hilit=extreme#p868863
xy-plane-71492.html?hilit=solving%20quadratic#p841486

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 08 Feb 2014
Posts: 3
Re: Is x greater than 1?  [#permalink]

Show Tags

New post 09 Feb 2014, 02:21
Question is x>1?

(1) (1/x)>- 1 --> (1+x)/x>0, two cases: (understood)

A. x>0 and 1+x>0, x>-1 (understood) --> x>0; (how do you get to this step?)

B. x<0 and 1+x<0, x<-1 --> x<-1. (understood)
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49968
Re: Is x greater than 1?  [#permalink]

Show Tags

New post 09 Feb 2014, 02:24
Catcat wrote:
Question is x>1?

(1) (1/x)>- 1 --> (1+x)/x>0, two cases: (understood)

A. x>0 and 1+x>0, x>-1 (understood) --> x>0; (how do you get to this step?)

B. x<0 and 1+x<0, x<-1 --> x<-1. (understood)


For A, we have that x>0 AND x>-1, whcih is the same as x>0 (intersection (common range) for x>0 and x>-1 is x>1).

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 08 Feb 2014
Posts: 3
Re: Is x greater than 1?  [#permalink]

Show Tags

New post 09 Feb 2014, 10:38
Bunuel wrote:
Catcat wrote:
Question is x>1?

For A, we have that x>0 AND x>-1, whcih is the same as x>0 (intersection (common range) for x>0 and x>-1 is x>1).

Hope it's clear.


Got it! Thank you for the clarification
Current Student
avatar
Joined: 21 May 2016
Posts: 16
Location: United Kingdom
GMAT 1: 730 Q49 V41
GPA: 3.5
Reviews Badge
Re: Is x greater than 1?  [#permalink]

Show Tags

New post 27 May 2016, 09:52
I don't understand Case B for statement 1 (why did you set x<0 when the equation sets it to greater than 0, \(\frac{1+x}{x}>0\) ?)

The same applies for Case B in statement 2.

I understand how the equation is constructed, but not why the inequality sign flips.

ALSO – can I confirm that multiplying both sides by x^2 for statement one and x^6 for statement two is possible (as regardless if x is negative, it will be positive as it has been squared?)

Thanks all, apologies if these are straightforward concepts.
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6956
Re: Is x greater than 1?  [#permalink]

Show Tags

New post 27 May 2016, 10:13
2
Judy1389 wrote:
I don't understand Case B for statement 1 (why did you set x<0 when the equation sets it to greater than 0, \(\frac{1+x}{x}>0\) ?)

The same applies for Case B in statement 2.

I understand how the equation is constructed, but not why the inequality sign flips.

ALSO – can I confirm that multiplying both sides by x^2 for statement one and x^6 for statement two is possible (as regardless if x is negative, it will be positive as it has been squared?)

Thanks all, apologies if these are straightforward concepts.



Hi,
If you have both numerator and denominator, they both are interlinked to give the SIGN to the fraction...
let me tell you by a easy example...
\(\frac{3}{4} >0\)....... it could be that the denominator is -ive and therefore numerator will also be -ive, so \(\frac{-3}{-4}> 0.\)...
here we are dealing with variable so we cannot say anything about the type of integer it is...
\(\frac{1+x}{x}>0\) .....
so first case is when both numerator and denominator are positive : +/+ = +>0...
second is when both are negative -/- = + >0...
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Current Student
avatar
Joined: 21 May 2016
Posts: 16
Location: United Kingdom
GMAT 1: 730 Q49 V41
GPA: 3.5
Reviews Badge
Re: Is x greater than 1?  [#permalink]

Show Tags

New post 27 May 2016, 10:44
Great, thank you that actually makes sense!

Can you comment re: multiplying both sides by an even square? (eg. x^2)

Posted from my mobile device
Intern
Intern
avatar
Joined: 27 May 2016
Posts: 3
Re: Is x greater than 1?  [#permalink]

Show Tags

New post 27 May 2016, 18:03
Let's consider the following scenarios :
X is positive then 1/x will always be greater than -1. (any positive number is greater than anything negative number)
X is a negative number whose absolute value is greater than 1 also satisfies (1). ( if X = -2 then 1/X = -0.5 which is greater than -1)

(2) 1/(x^5) > 1/(x^3)

Consider this :
X is and number greater than 1 then X^5 is greater than X^3, therefore, 1/(X^5) is less than 1/(X^3).
X is a positive number less than 1, then X^5 is less than X^3, therefore 1/(X^5) is greater than 1/(X^3)
X is a negative number less -1 then X^5 is less than X^3, therefore, 1/(X^5) is greater than 1/(X^3).
As you can see, the only values that satisfy (2) are the ones in which X<1, therefore (2) is sufficient. We know with absolute certainty that X IS NOT GREAT THAN 1.

answer is B.


Sent from my Z988 using GMAT Club Forum mobile app
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6956
Re: Is x greater than 1?  [#permalink]

Show Tags

New post 27 May 2016, 19:42
1
Judy1389 wrote:
Great, thank you that actually makes sense!

Can you comment re: multiplying both sides by an even square? (eg. x^2)

Posted from my mobile device



Hi,

yes you are correct...
Both ways it will amount to same..

1+x/x>0.....
same x>0, 1+x>0 OR x<0, 1+x<0..............

multiply by x^2....
(1+x)*x>0...
same cases will come up
same x>0, 1+x>0 OR x<0, 1+x<0..............
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Intern
Intern
avatar
Joined: 27 May 2016
Posts: 3
Re: Is x greater than 1?  [#permalink]

Show Tags

New post 27 May 2016, 20:56
This question requires logical reasoning instead of mathematical manipulation.

Statement 1: 1/x > -1. Let's multiply both sides by positive number, say x^2, then we get x>-(x^2). This is true for all positive numbers, since (-(x^2)) is negative. It's also true for all negative numbers whose absolute value is less than the absolute value of its square. Statement 1, therefore, is insufficient.

Statement 2: let's multiply both sides by x^4, we get 1/x > x, if x>1, then 1/x must be less than 1, but that's impossible because x>1. So, the only possible values for x are less than 1. Statement 2 is sufficient.

Sent from my Z988 using GMAT Club Forum mobile app
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6378
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: Is x greater than 1?  [#permalink]

Show Tags

New post 17 Apr 2018, 09:03
sandal85 wrote:
Is x greater than 1?

(1) 1/x >−1

(2) 1/x^5 > 1/x^3


Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
\(1/x > -1\)
\(⇔ x > - x^2\) by multiplying by \(x^2\)
\(⇔ x^2 + x > 0\)
\(⇔ x( x + 1 ) > 0\)
\(⇔ x < -1\) or \(x > 0\)

In inequality questions, the law “Question is King” tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient
Since the solution set of the question does not include that of condition 1), it is not sufficient.

Condition 2)
\(1/x^5 > 1/x^3\)
\(⇔ 1 > x^2\)
\(⇔ x^2 - 1 < 0\)
\(⇔ (x+1)(x-1) < 0\)
\(⇔ -1 < x < 1\)
The answer is "no".
Since ‘no’ is also a unique answer by CMT (Common Mistake Type) 1, the condition 2) is sufficient.

Therefore, B is the answer.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

GMAT Club Bot
Re: Is x greater than 1? &nbs [#permalink] 17 Apr 2018, 09:03
Display posts from previous: Sort by

Is x greater than 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®.