Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 05 Aug 2015
Posts: 55

Re: If x/x<x which of the following must be true about x? [#permalink]
Show Tags
21 Feb 2016, 14:46
Hi Karishma and other experts  I understand the solution but I'm still stuck on why reasoning is wrong. This is how I solved: x/x < x > x/x x > x*(1/x1)<0, so: 1. x<0; (1/x1)<0 > 1/x<1 > 1<x > x<1 THIS IS WHERE IT'S WRONG BUT WHY? 2. x>0; (1/x1)>0 > 1/x>1 > 1>x > 1>x THIS IS WHERE IT'S WRONG BUT WHY? Thank you!
_________________
Working towards 25 Kudos for the Gmatclub Exams  help meee I'm poooor



Current Student
Joined: 20 Mar 2014
Posts: 2683
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: If x/x<x which of the following must be true about x? [#permalink]
Show Tags
21 Feb 2016, 15:00
1
This post received KUDOS
happyface101 wrote: Hi Karishma and other experts  I understand the solution but I'm still stuck on why reasoning is wrong. This is how I solved:
x/x < x > x/x x > x*(1/x1)<0, so:
1. x<0; (1/x1)<0 > 1/x<1 > 1<x > x<1 THIS IS WHERE IT'S WRONG BUT WHY?
2. x>0; (1/x1)>0 > 1/x>1 > 1>x > 1>x THIS IS WHERE IT'S WRONG BUT WHY?
Thank you! The mistake you are making is in the portion with red text above. Your 'simplified' expression is x(1/x1) and not just (1/x1). Thus your cases become: Case 1: x<0 > x=x > x(1/x1)<0 > x(1/x1)<0 >x(1/x+1)>0 >x(1+x)/x > 0>x+1>0 >x>1 and this with the fact that x<0 > range becomes 1<x<0. Case 2: x>0 > x=x > x(1/x1)<0 > x(1/x1)<0 >x(1/x1)<0 >x(1x)/x < 0>1x<0 >x>1 and this with the fact that x>0 > range becomes x>1. Hope this helps.



Manager
Joined: 05 Aug 2015
Posts: 55

Re: If x/x<x which of the following must be true about x? [#permalink]
Show Tags
21 Feb 2016, 15:43
Engr2012 wrote: happyface101 wrote: Hi Karishma and other experts  I understand the solution but I'm still stuck on why reasoning is wrong. This is how I solved:
x/x < x > x/x x > x*(1/x1)<0, so:
1. x<0; (1/x1)<0 > 1/x<1 > 1<x > x<1 THIS IS WHERE IT'S WRONG BUT WHY?
2. x>0; (1/x1)>0 > 1/x>1 > 1>x > 1>x THIS IS WHERE IT'S WRONG BUT WHY?
Thank you! The mistake you are making is in the portion with red text above. Your 'simplified' expression is x(1/x1) and not just (1/x1). Thus your cases become: Case 1: x<0 > x=x > x(1/x1)<0 > x(1/x1)<0 >x(1/x+1)>0 >x(1+x)/x > 0>x+1>0 >x>1 and this with the fact that x<0 > range becomes 1<x<0. Case 2: x>0 > x=x > x(1/x1)<0 > x(1/x1)<0 >x(1/x1)<0 >x(1x)/x < 0>1x<0 >x>1 and this with the fact that x>0 > range becomes x>1. Hope this helps. Thank you so much! +1 I think the knowledge gap is that I treated x*(1/x1)<0 as if it's x*((1/x1)=0 In an inequality problem I obviously can't solve by taking the two apart and do x<0, (1/x1)<0 like I can for an equation. Thanks for helping me understand this!
_________________
Working towards 25 Kudos for the Gmatclub Exams  help meee I'm poooor



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7955
Location: Pune, India

Re: If x/x<x which of the following must be true about x? [#permalink]
Show Tags
21 Feb 2016, 21:14
2
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
happyface101 wrote: Engr2012 wrote: happyface101 wrote: Hi Karishma and other experts  I understand the solution but I'm still stuck on why reasoning is wrong. This is how I solved:
x/x < x > x/x x > x*(1/x1)<0, so:
1. x<0; (1/x1)<0 > 1/x<1 > 1<x > x<1 THIS IS WHERE IT'S WRONG BUT WHY?
2. x>0; (1/x1)>0 > 1/x>1 > 1>x > 1>x THIS IS WHERE IT'S WRONG BUT WHY?
Thank you! The mistake you are making is in the portion with red text above. Your 'simplified' expression is x(1/x1) and not just (1/x1). Thus your cases become: Case 1: x<0 > x=x > x(1/x1)<0 > x(1/x1)<0 >x(1/x+1)>0 >x(1+x)/x > 0>x+1>0 >x>1 and this with the fact that x<0 > range becomes 1<x<0. Case 2: x>0 > x=x > x(1/x1)<0 > x(1/x1)<0 >x(1/x1)<0 >x(1x)/x < 0>1x<0 >x>1 and this with the fact that x>0 > range becomes x>1. Hope this helps. Thank you so much! +1 I think the knowledge gap is that I treated x*(1/x1)<0 as if it's x*((1/x1)=0 In an inequality problem I obviously can't solve by taking the two apart and do x<0, (1/x1)<0 like I can for an equation. Thanks for helping me understand this! Additionally, you can split the factors as you did but you made an error there. x*(1/x1)<0 implies that x*(1/x1) is negative. So either x is negative and (1/x1) is positive or x is positive and (1/x1) is negative Case 1: x is negative and (1/x1) is positive When x is negative, x = x (1/x1) > 0 (1/(x)  1) > 0 1/x + 1 < 0 (1+x)/x < 0 1 < x< 0 Case 2: x is positive and (1/x1) is negative When x is positive, x = x (1/x1) < 0 (1/x  1) < 0 (1  x)/x < 0 (x  1)/x > 0 x > 1 or x < 0 But x is positive so x cannot be less than 0. So x > 1.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Manager
Joined: 24 May 2013
Posts: 85

Re: If x/x<x which of the following must be true about x? [#permalink]
Show Tags
14 Mar 2016, 22:00
x/x<x which of the following must be true about x? The range of values of x satisfying the above equation are shown in the image. 1<x<0 and x>1 (A) x>1 : From the figure, it is clear that for x>1 the given equation x/x<x always holds true. A may be the answer.(B) x>−1: This range contains a set 0<x<1 which makes x/x<x not true. For Ex x=1/2 doesn't satisfy the equation. (C) x<1: Contains x=1/2 which doesnot satisfy x/x<x . (D) x=1: x=1 doesnot satisfy x/x<x . (E) x2>1:This range contains set of values x<1 which makes x/x<x not true. For Ex x=4 doesn't satisfy the equation. May plz guide me if not taken the question in right way.
Attachments
xIIxI.png [ 7.27 KiB  Viewed 874 times ]



Intern
Joined: 17 Nov 2015
Posts: 9
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.73
WE: Business Development (Energy and Utilities)

Re: If x/x<x which of the following must be true about x? [#permalink]
Show Tags
06 Jun 2016, 21:17
If the given answer B has to be correct. i.e., x > 1
then x = 1 should satisfy.
x/mod (x) < x 1/mod(1)<1 which is not correct.



Intern
Joined: 25 Jul 2012
Posts: 19

Re: If x/x<x which of the following must be true about x? [#permalink]
Show Tags
09 Jun 2016, 04:36
My previous concept got completed squashed when I solved this problem.
I always take the value which overlap. For example: x > 2 AND x < 7; overlapping area includes 3, 4, 5 and 6.
Similarly: for x>1 (when x is positive) OR −1<x<0 (when x is negative), I don't see any overlap. Am I missing the word OR here? Definitely not.
I am still clueless how come x>1 is the solution for x>1 OR −1<x<0. If we take x>1, then x can also be = 0 and in that case the inequality will be meaning less because we will have 0 in the denominator.
Bunnuel  Please help. Not sure what I am missing here.



Current Student
Joined: 20 Mar 2014
Posts: 2683
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: If x/x<x which of the following must be true about x? [#permalink]
Show Tags
09 Jun 2016, 06:51
gauraku wrote: My previous concept got completed squashed when I solved this problem.
I always take the value which overlap. For example: x > 2 AND x < 7; overlapping area includes 3, 4, 5 and 6.
Similarly: for x>1 (when x is positive) OR −1<x<0 (when x is negative), I don't see any overlap. Am I missing the word OR here? Definitely not.
I am still clueless how come x>1 is the solution for x>1 OR −1<x<0. If we take x>1, then x can also be = 0 and in that case the inequality will be meaning less because we will have 0 in the denominator.
Bunnuel  Please help. Not sure what I am missing here. This question of yours will trip you on other MUST BE TRUE questions. A fool proof way to solve any MBT question is to realize that the correct answer will be true for ALL values while the incorrect options will fail at 1 or more than 1 possible values. I always recommend that for MBT questions, eliminate incorrect ones to arrive at the correct answer. Coming back to this question, for your doubt x>1 satisfies both the posisble ranges : 1<x<0 and x>1 and this is the reason why this option is the correct one. Other options are either partically covering these 2 ranges or none at all. Let us try to use process of elimination (POE) to eliminate the other 4 incorrect options. (A) \(x>1\) > what about x=0.5, this value satisfies the given equation x/x<x but is not covered by this option. Eliminate.(B) \(x>1\) (C) \(x<1\)> this translates to 1<x<1, what about x=2, this value satisfies the given equation x/x<x but is not covered by this option. Eliminate.(D) \(x=1\) > this translates to x= 1 or 1, what about x=0.5, this value satisfies the given equation x/x<x but is not covered by this option. Eliminate.(E) \(x^2>1\) > what about x=0.5, this value satisfies the given equation x/x<x but is not covered by this option. Eliminate.Thus, only option B is left and is thus the correct answer. I see your point that 0<x<1 isnt a correct range but you can surely say that if 1<x<0 OR x>1 then ALL values of x in these 2 ranges will be >1. Thus x>1 is the MBT condition for this question. Hope this helps.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7955
Location: Pune, India

Re: If x/x<x which of the following must be true about x? [#permalink]
Show Tags
09 Jun 2016, 19:56
gauraku wrote: My previous concept got completed squashed when I solved this problem.
I always take the value which overlap. For example: x > 2 AND x < 7; overlapping area includes 3, 4, 5 and 6.
Similarly: for x>1 (when x is positive) OR −1<x<0 (when x is negative), I don't see any overlap. Am I missing the word OR here? Definitely not.
I am still clueless how come x>1 is the solution for x>1 OR −1<x<0. If we take x>1, then x can also be = 0 and in that case the inequality will be meaning less because we will have 0 in the denominator.
Bunnuel  Please help. Not sure what I am missing here. I have taken this issue in detail in this post: http://www.veritasprep.com/blog/2012/07 ... andsets/
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Manager
Joined: 03 Jul 2015
Posts: 70
Concentration: Marketing, Finance

Re: If x/x<x which of the following must be true about x? [#permalink]
Show Tags
11 Jun 2016, 04:10
durgesh79 wrote: i think OA is correct....
the question is If x / x < x. so we have to consider only those values of x for which this inequalty is true and what are those values 1. when x is between 1 and 0 2. when x is more than 1
lets call these conditions our universe.
Now the question is for all values of x (in our universe) which of the following is true option B, x > 1, has both conditions 1 and 2
now you may say what about x = 1/2 .... that wasnt even part of our universe... so even if x = 1/2 is satisfying option B and not the question stem, we dont have to worry... becuase we are not supposed to take it as an example ...
for all values of x in our universe, option B is ALWAYS true... Option A is not always true... 1<x<0 and x>1 are the two areas where x can lie. How can B be correct while we have answer choice like A(x>1) . x>1 tells that x can even be 0.5 but the range we found out does not say the same. Plz clarify.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7955
Location: Pune, India

Re: If x/x<x which of the following must be true about x? [#permalink]
Show Tags
12 Jun 2016, 20:53
sa18 wrote: durgesh79 wrote: i think OA is correct....
the question is If x / x < x. so we have to consider only those values of x for which this inequalty is true and what are those values 1. when x is between 1 and 0 2. when x is more than 1
lets call these conditions our universe.
Now the question is for all values of x (in our universe) which of the following is true option B, x > 1, has both conditions 1 and 2
now you may say what about x = 1/2 .... that wasnt even part of our universe... so even if x = 1/2 is satisfying option B and not the question stem, we dont have to worry... becuase we are not supposed to take it as an example ...
for all values of x in our universe, option B is ALWAYS true... Option A is not always true... 1<x<0 and x>1 are the two areas where x can lie. How can B be correct while we have answer choice like A(x>1) . x>1 tells that x can even be 0.5 but the range we found out does not say the same. Plz clarify. This same question has been asked many times in this thread and has been responded to time and again. You need to go through the thread. Right above your post, I have given the link where this concept is discussed in detail. Also, focus on the question stem: which of the following must be true about x? which means: which option must be true about ALL values that x can take? Will ALL value of x be greater than 1? No. (A) incorrect. Will ALL values of x be greater than 1? Yes. (B) correct.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Manager
Joined: 11 Apr 2016
Posts: 53
Location: India
Concentration: Marketing, Technology
WE: Business Development (Computer Software)

Re: If x/x<x which of the following must be true about x? [#permalink]
Show Tags
09 Mar 2017, 09:17
In option B, since it states x>1, x could be 0.
Then the expression x/x<x will not stand true. Then how is option B the right answer?



Math Expert
Joined: 02 Sep 2009
Posts: 43891

Re: If x/x<x which of the following must be true about x? [#permalink]
Show Tags
09 Mar 2017, 09:29



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2016

Re: If x/x<x which of the following must be true about x? [#permalink]
Show Tags
15 Mar 2017, 15:41
nmohindru wrote: If \(\frac{x}{x}<x\) which of the following must be true about \(x\)?
(A) \(x>1\)
(B) \(x>1\)
(C) \(x<1\)
(D) \(x=1\)
(E) \(x^2>1\) We can safely say that x ≠ 0 since x is in the denominator. Since x ≠ 0: 1) x/x = 1 if x is positive, or 2) x/x = 1 if x is negative Therefore, if x is positive, then 1 < x, i.e., x > 1, and if x is negative, then 1 < x, i.e., x > 1. So, we have x > 1 or x > 1. Since, if x is greater than 1, x is also greater than 1, choice B is the correct answer. Answer: B
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Manager
Joined: 22 Mar 2014
Posts: 151
Location: United States
Concentration: Finance, Operations
GPA: 3.91
WE: Information Technology (Computer Software)

Re: If x/x<x which of the following must be true about x? [#permalink]
Show Tags
16 Mar 2017, 07:28
Bunuel wrote: nmohindru wrote: If \(\frac{x}{x}<x\) which of the following must be true about \(x\)?
(A) \(x>1\)
(B) \(x>1\)
(C) \(x<1\)
(D) \(x=1\)
(E) \(x^2>1\) This question was well explained by Durgesh and Ian Stewart, but since there are still some doubts, I'll try to add my 2 cents. First of all let's solve this inequality step by step and see what is the solution for it, or in other words let's see in which ranges this inequality holds true. Two cases for \(\frac{x}{x}<x\): A. \(x<0\) > \(x=x\) > \(\frac{x}{x}<x\) > \(1<x\) > \(1<x<0\); B. \(x>0\) > \(x=x\) > \(\frac{x}{x}<x\) > \(1<x\). So given inequality holds true in the ranges: \(1<x<0\) and \(x>1\). Which means that \(x\) can take values only from these ranges. {1} xxxx{0}{1} xxxxxxNow, we are asked which of the following must be true about \(x\). Option A can not be ALWAYS true because \(x\) can be from the range \(1<x<0\), eg \(\frac{1}{2}\) and \(x=\frac{1}{2}<1\). Only option which is ALWAYS true is B. ANY \(x\) from the ranges \(1<x<0\) and \(x>1\) will definitely be more the \(1\), all "red", possible xes are to the right of 1, which means that all possible xes are more than 1. Answer: B. Hi Bunuel, I have a doubt here. For 0<x<1, the condition does not hold. So why we are taking the range X > 1 instead of X > 1 when we know for X > 1, we also have 0<X<1 range.



Math Expert
Joined: 02 Sep 2009
Posts: 43891

Re: If x/x<x which of the following must be true about x? [#permalink]
Show Tags
16 Mar 2017, 08:29
arunavamunshi1988 wrote: Bunuel wrote: nmohindru wrote: If \(\frac{x}{x}<x\) which of the following must be true about \(x\)?
(A) \(x>1\)
(B) \(x>1\)
(C) \(x<1\)
(D) \(x=1\)
(E) \(x^2>1\) This question was well explained by Durgesh and Ian Stewart, but since there are still some doubts, I'll try to add my 2 cents. First of all let's solve this inequality step by step and see what is the solution for it, or in other words let's see in which ranges this inequality holds true. Two cases for \(\frac{x}{x}<x\): A. \(x<0\) > \(x=x\) > \(\frac{x}{x}<x\) > \(1<x\) > \(1<x<0\); B. \(x>0\) > \(x=x\) > \(\frac{x}{x}<x\) > \(1<x\). So given inequality holds true in the ranges: \(1<x<0\) and \(x>1\). Which means that \(x\) can take values only from these ranges. {1} xxxx{0}{1} xxxxxxNow, we are asked which of the following must be true about \(x\). Option A can not be ALWAYS true because \(x\) can be from the range \(1<x<0\), eg \(\frac{1}{2}\) and \(x=\frac{1}{2}<1\). Only option which is ALWAYS true is B. ANY \(x\) from the ranges \(1<x<0\) and \(x>1\) will definitely be more the \(1\), all "red", possible xes are to the right of 1, which means that all possible xes are more than 1. Answer: B. Hi Bunuel, I have a doubt here. For 0<x<1, the condition does not hold. So why we are taking the range X > 1 instead of X > 1 when we know for X > 1, we also have 0<X<1 range. This issue has been addressed MANY times in previous 5 (!) pages. Please read the thread before posting a question. Thank you.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 05 Jan 2017
Posts: 434
Location: India

Re: If x/x<x which of the following must be true about x? [#permalink]
Show Tags
17 Mar 2017, 02:13
put test values as 2, 0.5, 0.5, 2 for 2, x/x >x for 0.5, x/ x <x for 0.5, x/x >x
thereore Option A i.e. x>1 holds true



Math Expert
Joined: 02 Sep 2009
Posts: 43891

Re: If x/x<x which of the following must be true about x? [#permalink]
Show Tags
17 Mar 2017, 02:16
ByjusGMATapp wrote: put test values as 2, 0.5, 0.5, 2 for 2, x/x >x for 0.5, x/ x <x for 0.5, x/x >x
thereore Option A i.e. x>1 holds true Please note that the correct answer is B, not A.
_________________
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? Extrahard Quant Tests with Brilliant Analytics




Re: If x/x<x which of the following must be true about x?
[#permalink]
17 Mar 2017, 02:16



Go to page
Previous
1 2 3 4 5
[ 98 posts ]



