Author 
Message 
TAGS:

Hide Tags

Senior Manager
Status: May The Force Be With Me (DDAY 15 May 2012)
Joined: 06 Jan 2012
Posts: 268
Location: India
Concentration: General Management, Entrepreneurship

If x≠0, is x < 1 ? (1) x^2< 1 (2) x < 1/x [#permalink]
Show Tags
08 Apr 2012, 08:43
5
This post received KUDOS
32
This post was BOOKMARKED
Question Stats:
60% (01:10) correct 40% (01:15) wrong based on 1189 sessions
HideShow timer Statistics
If x≠0, is x < 1 ? (1) x^2 < 1 (2) x < 1/x
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Giving +1 kudos is a better way of saying 'Thank You'.
Last edited by Bunuel on 08 Apr 2012, 09:02, edited 1 time in total.
Edited the question



Math Expert
Joined: 02 Sep 2009
Posts: 43903

Re: If x≠0, is x <1? [#permalink]
Show Tags
08 Apr 2012, 09:01
14
This post received KUDOS
Expert's post
18
This post was BOOKMARKED
boomtangboy wrote: If x≠0, is x <1? (1) x2<1 (2) x < 1/x If \(x\neq{0}\), is \(x <1\)?Is \(x <1\)? > is \(1<x<1\) (\(x\neq{0}\))? (1) \(x^2<1\) > \(1<x<1\). Sufficient. (2) \(x < \frac{1}{x}\) > since LHS (x) is an absolute value which is always nonnegative then RHS (1/x), must be positive (as \(x < \frac{1}{x}\)), so \(\frac{1}{x}>0\) > \(x>0\). Now, if \(x>0\) then \(x=x\) and we have: \(x<\frac{1}{x}\) > since \(x>0\) then we can safely multiply both parts by it: \(x^2<1\) > \(1<x<1\), but as \(x>0\), the final range is \(0<x<1\). Sufficient. Answer D.
_________________
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



Manager
Joined: 14 Feb 2012
Posts: 226

Re: If x≠0, is x <1? [#permalink]
Show Tags
19 Apr 2012, 12:25
My answer was A... Explanation> x<1 means x should be between 1 and 1. from (1) x21<0 => x between 1 and 1. sufficient from (2) if x +ve then same as 1 and sufficient if x ve then x=x x2<1 or x2 > 1 not sufficient so and A Please correct me if wrong
_________________
The Best Way to Keep me ON is to give Me KUDOS !!! If you Like My posts please Consider giving Kudos
Shikhar



Math Expert
Joined: 02 Sep 2009
Posts: 43903

Re: If x≠0, is x < 1 ? (1) x^2< 1 (2) x < 1/x [#permalink]
Show Tags
19 Apr 2012, 20:44



Intern
Joined: 01 Mar 2012
Posts: 28
Concentration: Operations, Finance
GPA: 3.3
WE: Engineering (Manufacturing)

Re: If x≠0, is x < 1 ? (1) x^2< 1 (2) x < 1/x [#permalink]
Show Tags
23 Apr 2012, 19:41
Bunuel wrote: shikhar wrote: If x≠0, is x <1?
(1) x2<1 (2) x < 1/x Merging similar topics. shikhar wrote: My answer was A... Explanation> x<1 means x should be between 1 and 1.
from (1) x21<0 => x between 1 and 1. sufficient
from (2) if x +ve then same as 1 and sufficient if x ve then x=x x2<1 or x2 > 1 not sufficient
so and A
Please correct me if wrong \(x\) cannot be negative. Refer to the solution above. Also if \(x<0\) then we have \(x<\frac{1}{x}\) and now if we cross mulitply by negative \(x\) then we should flip the sign: \(x^2>1\) > \(x^2+1<0\) which cannot be true for any real value of \(x\) (the sum of two positive value cannot be less than zero). Well Explained Bunuel



Math Expert
Joined: 02 Sep 2009
Posts: 43903

Re: If x≠0, is x < 1 ? (1) x^2< 1 (2) x < 1/x [#permalink]
Show Tags
04 Jul 2013, 00:24



Director
Joined: 25 Apr 2012
Posts: 721
Location: India
GPA: 3.21
WE: Business Development (Other)

Re: If x≠0, is x < 1 ? (1) x^2< 1 (2) x < 1/x [#permalink]
Show Tags
04 Jul 2013, 04:16
1
This post received KUDOS
boomtangboy wrote: If x≠0, is x < 1 ?
(1) x^2 < 1 (2) x < 1/x Given question stem asks if x<1> Is 1<x<1 from St 1 we have x^2<1 > 1<x<1 So Sufficient from St2 we have x<1/x Notice that x is a positive value and for any Integer value x> 1/x This implies X is a fraction. In order to satisfy the above equation let us take some fractional value of x and check what happens to the above equation x= 1/2 so we have 1/2<2 No x=3/4 so we have 3/4< 4/3 Yes x=4/3 so we have 4/3 <3/4  no We see that when fraction is between 0<x<1 then the above equation holds true and hence x is between 1 and 1 Ans should be D.... Bunuel's solution is superb. Saves time
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”



Senior Manager
Joined: 13 May 2013
Posts: 456

Re: If x≠0, is x < 1 ? (1) x^2< 1 (2) x < 1/x [#permalink]
Show Tags
04 Jul 2013, 11:25
1
This post received KUDOS
If x≠0, is x < 1 ?
is x<1 OR is x<1 x>1
Is 1<x<1?
(1) x^2 < 1 x^2<1 x<1
This tells us exactly what the stem looks for. SUFFICIENT
(2) x < 1/x is x < 1/x OR is x < 1/x is x > 1/x SO 1/x < x < 1/x 1 < x^2 < 1 SUFFICIENT
(I am going to use Bunuel's method only because I think it makes more sense and I believe mine is wrong anyways)
x<1/x if x<1/x then 1/x MUST be positive as it is greater than an absolute value. If 1/x is positive then x must also be positive and therefore x<1/x is actually equal to x<1/x. Because we know that x is positive we can multiply both sides by x to simplify.
(x)* x < 1/x *(x) x^2 < 1 x<1 x<1 or x>1 1<x<1
This tells us exactly what the stem is looking for SUFFICIENT (D)
(also, could someone explain to me how to solve by the method I originally chose in #2...the one where I get the positive and negative case for X)
Thanks!



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 625

Re: If x≠0, is x < 1 ? (1) x^2< 1 (2) x < 1/x [#permalink]
Show Tags
04 Jul 2013, 12:00
1
This post received KUDOS
WholeLottaLove wrote: If x≠0, is x < 1 ?
(also, could someone explain to me how to solve by the method I originally chose in #2...the one where I get the positive and negative case for X)
Thanks! I.x>0 \(x<\frac{1}{x}\) As x>0, we can safely crossmultiply \(\to x^2<1 \to x<1.\) II.x<0 \(x<\frac{1}{x}\) multiply both sides by\(x^2\), which is a positive quantity \(\to x^3<x\)\([x\neq{0}]\) or \(x(1+x^2)>0 \to\) \((1+x^2)\) and x have same sign and as\((1+x^2)\) is always positive, thus x>0. However, this goes against our assumption. Thus, x is not negative. Sufficient.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Senior Manager
Joined: 13 May 2013
Posts: 456

Re: If x≠0, is x < 1 ? (1) x^2< 1 (2) x < 1/x [#permalink]
Show Tags
07 Jul 2013, 17:54
If x≠0, is x < 1 ?
(1) x^2 < 1 x<1, x>1 1<x<1
Valid X is a number that is greater than 1 (i.e. 3/4, 1/2) and less than 1 (i.e. 1/2, 3/4) either way the absolute value of any of those numbers will be less than 1. SUFFICIENT
(2) x < 1/x Multiply both sides by x x^2<1 Same solution as above. SUFFICIENT
(D)
Is it valid to multiply the absolute value of x on one side (like in number two) to simplify as long as x is positive?



Math Expert
Joined: 02 Sep 2009
Posts: 43903

Re: If x≠0, is x < 1 ? (1) x^2< 1 (2) x < 1/x [#permalink]
Show Tags
07 Jul 2013, 22:18
1
This post received KUDOS
Expert's post
1
This post was BOOKMARKED



Senior Manager
Joined: 13 May 2013
Posts: 456

Re: If x≠0, is x < 1 ? (1) x^2< 1 (2) x < 1/x [#permalink]
Show Tags
08 Jul 2013, 15:39
It helps a lot. Thanks! Bunuel wrote: WholeLottaLove wrote: If x≠0, is x < 1 ?
(1) x^2 < 1 x<1, x>1 1<x<1
Valid X is a number that is greater than 1 (i.e. 3/4, 1/2) and less than 1 (i.e. 1/2, 3/4) either way the absolute value of any of those numbers will be less than 1. SUFFICIENT
(2) x < 1/x Multiply both sides by x x^2<1 Same solution as above. SUFFICIENT
(D)
Is it valid to multiply the absolute value of x on one side (like in number two) to simplify as long as x is positive? As, since from x < 1/x we concluded that x is positive, then yes we can do that: x < 1/x > x^2 < 1. Hope it helps.



Manager
Joined: 14 Jan 2013
Posts: 151
Concentration: Strategy, Technology
GMAT Date: 08012013
GPA: 3.7
WE: Consulting (Consulting)

Re: If x≠0, is x < 1 ? (1) x^2< 1 (2) x < 1/x [#permalink]
Show Tags
21 Jul 2013, 19:38
Bunuel wrote: shikhar wrote: If x≠0, is x <1?
(1) x2<1 (2) x < 1/x Merging similar topics. shikhar wrote: My answer was A... Explanation> x<1 means x should be between 1 and 1.
from (1) x21<0 => x between 1 and 1. sufficient
from (2) if x +ve then same as 1 and sufficient if x ve then x=x x2<1 or x2 > 1 not sufficient
so and A
Please correct me if wrong \(x\) cannot be negative. Refer to the solution above. Also if \(x<0\) then we have \(x<\frac{1}{x}\) and now if we cross mulitply by negative \(x\) then we should flip the sign: \(x^2>1\) > \(x^2+1<0\) which cannot be true for any real value of \(x\) (the sum of two positive value cannot be less than zero). Bunuel, I am not clear with this part Also if x<0 then we have x<\frac{1}{x} and now if we cross mulitply by negative x then we should flip the sign: x^2>1 > x^2+1<0I am getting the below: x < 1/x > when we cross multiply by ve x, we get (x*x ) x2 >( flipping) 1 ( x/x) > X2+1 >0 ?? Pls help...
_________________
"Where are my Kudos" ............ Good Question = kudos
"Start enjoying all phases" & all Sections
__________________________________________________________________ http://gmatclub.com/forum/collectionofarticlesoncriticalreasoning159959.html
http://gmatclub.com/forum/percentages700800levelquestions130588.html
http://gmatclub.com/forum/700to800levelquantquestionwithdetailsoluition143321.html



Math Expert
Joined: 02 Sep 2009
Posts: 43903

Re: If x≠0, is x < 1 ? (1) x^2< 1 (2) x < 1/x [#permalink]
Show Tags
21 Jul 2013, 20:44
Mountain14 wrote: Bunuel wrote: shikhar wrote: If x≠0, is x <1?
(1) x2<1 (2) x < 1/x Merging similar topics. shikhar wrote: My answer was A... Explanation> x<1 means x should be between 1 and 1.
from (1) x21<0 => x between 1 and 1. sufficient
from (2) if x +ve then same as 1 and sufficient if x ve then x=x x2<1 or x2 > 1 not sufficient
so and A
Please correct me if wrong \(x\) cannot be negative. Refer to the solution above. Also if \(x<0\) then we have \(x<\frac{1}{x}\) and now if we cross mulitply by negative \(x\) then we should flip the sign: \(x^2>1\) > \(x^2+1<0\) which cannot be true for any real value of \(x\) (the sum of two positive value cannot be less than zero). Bunuel, I am not clear with this part Also if x<0 then we have x<\frac{1}{x} and now if we cross mulitply by negative x then we should flip the sign: x^2>1 > x^2+1<0I am getting the below: x < 1/x > when we cross multiply by ve x, we get (x*x ) x2 >( flipping) 1 ( x/x) > X2+1 >0 ?? Pls help... When I say "multiply by negative x", I mean multiply by x, which is negative, so simply by x.
_________________
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



CR Forum Moderator
Status: The best is yet to come.....
Joined: 10 Mar 2013
Posts: 529

Re: If x≠0, is x < 1 ? (1) x^2< 1 (2) x < 1/x [#permalink]
Show Tags
22 May 2014, 19:33
If x <1 > 1<x<1, why not x < 1/x > 1/x<x<1/x? If so, how does it lead to x>0?
_________________
Hasan Mahmud



Intern
Joined: 20 May 2014
Posts: 37
Location: India

Re: If x≠0, is x < 1 ? (1) x^2< 1 (2) x < 1/x [#permalink]
Show Tags
22 May 2014, 22:19
3
This post received KUDOS
1
This post was BOOKMARKED
Hi Mahmud, x <1 can be written as 1<x<1 because 1 is a constant BUTx < \(\frac{1}{x}\) cannot be written as 1/x<x<1/x because 1/x is a variableSolving, x <\(\frac{1}{x}\) RHS has to be greater than 0 (As LHS can only be +ve or 0) => \(\frac{1}{x}\) > 0 => x>0 (x cannot be ve or 0 , Because, if x is ve then \(\frac{1}{x}\) is ve if x = 0 then\(\frac{1}{x}\) is not defined)Rgds, Rajat
_________________
If you liked the post, please press the'Kudos' button on the left



Manager
Status: Please do not forget to give kudos if you like my post
Joined: 19 Sep 2008
Posts: 118
Location: United States (CA)

Re: If x≠0, is x < 1 ? (1) x^2< 1 (2) x < 1/x [#permalink]
Show Tags
18 Oct 2014, 12:22
X cannot be 0. 1. X^2 < 1 ==> X < 1 since X^2 cannot be negative value so both positive and negative values are possible for X. Sufficient. 2. if X=1 then 1<1 not possible X cannot be 0 so X > 0. X^2 < 1 same as st1. Sufficient. ANSWER: D boomtangboy wrote: If x≠0, is x < 1 ?
(1) x^2 < 1 (2) x < 1/x
_________________
Please Help with Kudos, if you like my post.



Senior Manager
Joined: 08 Dec 2015
Posts: 314

Re: If x≠0, is x < 1 ? (1) x^2< 1 (2) x < 1/x [#permalink]
Show Tags
10 Sep 2016, 07:34
Hi Bunuel!
A question here.
How is St 2 sufficient? You say it yourself that 2) implies that 0<x<1 so that is just part of the range of the question stem ( is 1<x<1 ?) So statement two doesn't cover the negative area of the range. How can it be considered to be sufficient?
Do I make myself clear btw?



Math Expert
Joined: 02 Sep 2009
Posts: 43903

Re: If x≠0, is x < 1 ? (1) x^2< 1 (2) x < 1/x [#permalink]
Show Tags
11 Sep 2016, 02:21



Manager
Joined: 22 Feb 2016
Posts: 102
Location: India
Concentration: Economics, Healthcare
GMAT 1: 690 Q42 V47 GMAT 2: 710 Q47 V39
GPA: 3.57

Re: If x≠0, is x < 1 ? (1) x^2< 1 (2) x < 1/x [#permalink]
Show Tags
30 Dec 2016, 07:05
Bunuel wrote: boomtangboy wrote: If x≠0, is x <1? (1) x2<1 (2) x < 1/x If \(x\neq{0}\), is \(x <1\)?Is \(x <1\)? > is \(1<x<1\) (\(x\neq{0}\))? (1) \(x^2<1\) > \(1<x<1\). Sufficient. (2) \(x < \frac{1}{x}\) > since LHS (x) is an absolute value which is always nonnegative then RHS (1/x), must be positive (as \(x < \frac{1}{x}\)), so \(\frac{1}{x}>0\) > \(x>0\). Now, if \(x>0\) then \(x=x\) and we have: \(x<\frac{1}{x}\) > since \(x>0\) then we can safely multiply both parts by it: \(x^2<1\) > \(1<x<1\), but as \(x>0\), the final range is \(0<x<1\). Sufficient. Answer D. Can we solve this by plugging in numbers? I did it that way and got the correct answer. Wondering if that was just by chance or was I correct in my approach




Re: If x≠0, is x < 1 ? (1) x^2< 1 (2) x < 1/x
[#permalink]
30 Dec 2016, 07:05



Go to page
1 2
Next
[ 23 posts ]



