Author 
Message 
TAGS:

Hide Tags

Director
Joined: 07 Jun 2004
Posts: 612
Location: PA

Is 1/(xy) < y  x [#permalink]
Show Tags
07 Jan 2011, 09:09
11
This post received KUDOS
21
This post was BOOKMARKED
Question Stats:
23% (03:24) correct
77% (04:04) wrong based on 880 sessions
HideShow timer Statistics
Is 1/(x  y) < y  x (1) 1/x < 1/y (2) 2x = 3y
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
If the Q jogged your mind do Kudos me : )
Last edited by Bunuel on 10 Jul 2013, 02:31, edited 2 times in total.
Edited the OA.



Manager
Joined: 07 Jun 2010
Posts: 86

Re: Tough DS Algebra [#permalink]
Show Tags
07 Jan 2011, 09:37
Proposition 1:
1/X < 1/Y
This is equal to X > Y  x, y both > 0 or both < 0
Case 1: Both > 0. X > Y, therefore XY >0 , YX <0, so 1/(XY) > 0 and YX<0 so FALSE
Case 2: X < 0, Y>0. Cross multiple and switch the signs, you get Y>X. There for YX>0, XY<0.
1/(XY)<0, YX>0, so case 2, 1/(XY) < (YX) is TRUE
Therefore statement 1 is insufficient by contradiction.
Proposition 2:
2X=3Y
Case 1: X=3, Y=2  therefore XY=1, YX = 1
1/(XY) < YX > 1/1 < 1 = FALSE
Case 2: X=3, Y=2  therefore XY=1, YX = 1
1/(XY) < YX > 1/1 < 1 = TRUE
Insufficient by contradicition
Both Statments together  Intutitively, neither statement removes the ambiguity of the sign of X or Y. I can't think of a proof.
Therefore answer is E.



Math Expert
Joined: 02 Sep 2009
Posts: 39753

Is 1/(xy) < y  x [#permalink]
Show Tags
07 Jan 2011, 10:15
16
This post received KUDOS
Expert's post
11
This post was BOOKMARKED
rxs0005 wrote: Is 1 / (xy) < y  x
1 / x < 1 / y
2x = 3y First of all if it were realistic GMAT question it would most likely state that \(xy\neq{0}\) and \(x\neq{y}\) (as x, y and xy are in denominators). Is \(\frac{1}{xy}<yx\)? > is \(\frac{1}{xy}+xy<0\) > is \(\frac{1+(xy)^2}{xy}<0\)? as the nominator (\(1+(xy)^2\)) is always positive then the question basically becomes whether denominator (\(xy\)) is negative > is \(xy<0\)? or is \(x<y\)? (1) \(\frac{1}{x}<\frac{1}{y}\) > if both unknowns are positive or both unknowns are negative then \(y<x\) (if both are positive cross multiply to get \(y<x\) and if both are negative cross multiply and flip the sigh twice to get \(y<x\) again) and the answer will be NO but if \(x<0<y\) given inequality also holds true and in this case the answer will be YES (if \(x\) is any negative number and \(y\) is any positive number then \(\frac{1}{x}=negative<positive=\frac{1}{y}\)). Not sufficient. (2) \(2x=3y\) > \(x\) and \(y\) have the same sign, next: \(\frac{x}{y}=\frac{3}{2}\): if both \(x\) and \(y\) are positive (for example 3 and 2 respectively) then \(0<y<x\) and the answer will be NO but if both \(x\) and \(y\) are negative (for example 3 and 2 respectively) then \(x<y<0\) and the answer will be YES. Not sufficient. (1)+(2) As from (2) \(x\) and \(y\) have the same sign then from (1) \(y<x\) and the answer to the question is NO. Sufficient. Answer: C.
_________________
New to the Math Forum? Please read this: 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: 20 Jul 2011
Posts: 145
GMAT Date: 10212011

Re: Tough DS Algebra [#permalink]
Show Tags
07 Sep 2011, 04:24
** Quote: Is 1 / (xy) < y  x?
1. 1 / x < 1 / y 2. 2x = 3y equation: \(\frac{1}{(xy)} < yx\) Statement 1Given \(\frac{1}{x}<\frac{1}{y}\), we have 2 possibilities: One: if both x and y share the same signs (i.e. both are positive or both are negative) > y<xleft side of equation will be a positive fraction; right side will be negative integer > equation = true Two: if x is negative and y is positive (e.g. x=2 and y=3), left side of equation will be negative fraction; right side will be positive integer > equation = false Insufficient. Statement 2Given 2x=3y > x/y = 3/2 >i.e. x and y share the same sign (i.e. both positive or both negative). 2 possibilities: One: if both x and y are positive (i.e. x=3, y=2), results in 1/1 < 1 > equation = falseTwo: if both x and y are negative (i.e. x=3, y=2), results in 1/1 < 1 > equation = true Insufficient. Statement 1 + 2Applying statement 2 and 1 together, we know that x and y: i. share the same sign, and ii. that y<x > which means, equation = false i.e. No Sufficient. Answer: C
_________________
"The best day of your life is the one on which you decide your life is your own. No apologies or excuses. No one to lean on, rely on, or blame. The gift is yours  it is an amazing journey  and you alone are responsible for the quality of it. This is the day your life really begins."  Bob Moawab



Retired Moderator
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1657
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs

Is 1/(xy) < y  x? [#permalink]
Show Tags
27 Aug 2012, 07:45
Is \(\frac{1}{(xy)} < y  x\) ? (1) \(\frac{1}{x} < \frac{1}{y}\) (2) \(2x = 3y\) I don't agree with the OA. It must be C. If \(2x = 3y\), then \(x\) and \(y\)are both positive or both negative. So, if we know that: \(\frac{1}{x} < \frac{1}{y}\), then \(x>y\) > \(x y > 0\) With that information we can conclude that the answer is No. C is correct. Please, your comments.
_________________
"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."
My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/myirlogbookdiary133264.html
GMAT Club Premium Membership  big benefits and savings



Math Expert
Joined: 02 Sep 2009
Posts: 39753

Re: Is 1/(xy) < y  x? [#permalink]
Show Tags
27 Aug 2012, 08:14



Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)

Re: Is 1 / (xy) < y  x [#permalink]
Show Tags
03 Sep 2012, 05:16
5
This post received KUDOS
rxs0005 wrote: Is 1 / (xy) < y  x
(1) 1 / x < 1 / y (2) 2x = 3y If we denote by \(A=xy\), the question is "Is \(\frac{1}{A}<A?\)" If \(A>0\), the above inequality cannot hold (a positive number is not smaller than a negative number). So, the question can be reworded as is \(A<0\), or is \(xy<0\) which is the same as is \(x<y?\) (1) The given inequality is equivalent to \(\frac{xy}{xy}>0.\) If \(xy>0\), or in other words if \(x\) and \(y\) have the same sign, then necessarily \(x\) must be greater than \(y.\) If \(xy<0\), or in other words if \(x\) and \(y\) have opposite signs, then necessarily \(x\) must be smaller than \(y.\) Not sufficient. (2) \(x=\frac{3}{2}y.\) If \(y<0\), then \(x<y.\) But if \(y>0,\) then \(x>y.\) Not sufficient. (1) and (2) together: Since from (2) we have that \(x\) and \(y\) have the same sign, using (1) we deduce that necessarily \(xy>0.\) So, the answer to the question "Is \(x<y\)" is a definite NO. Sufficient. Answer C.
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Manager
Status: Do till 740 :)
Joined: 13 Jun 2011
Posts: 110
Concentration: Strategy, General Management
GPA: 3.6
WE: Consulting (Computer Software)

Re: Is 1 / (xy) < y  x [#permalink]
Show Tags
25 Nov 2012, 19:54
Hi Buneul,
Can you please explain this part? if both are negative cross multiply and flip the sigh twice to get y<x again)



Math Expert
Joined: 02 Sep 2009
Posts: 39753

Re: Is 1 / (xy) < y  x [#permalink]
Show Tags
26 Nov 2012, 02:28



Manager
Joined: 28 Dec 2012
Posts: 111
Location: India
Concentration: Strategy, Finance
WE: Engineering (Energy and Utilities)

Re: Is 1 / (xy) < y  x [#permalink]
Show Tags
14 Jan 2013, 06:16
stem reduces to Is x<y ? [1/(yx) = (yx) => (yx) >0 ] A. Depends on sign of x,y. (both positive or both negative for eg. Vs positivenegative give both YES and NO) B. x= 3k, y= 2k. K>=0, Answer NO. K<0 Answer is YES. C. Using 2. x =3k when y =2k. using the above in 1. 1/x < 1/ y or 1/3k < 1/2k holds only for k>0. For k>0, Using 2, we definitely get the single answer as NO. KUDOS, if YOU LIKE
_________________
Impossibility is a relative concept!!



Director
Joined: 25 Apr 2012
Posts: 728
Location: India
GPA: 3.21
WE: Business Development (Other)

Re: Tough DS Algebra [#permalink]
Show Tags
14 Jan 2013, 23:43
Bunuel wrote: rxs0005 wrote: Is 1 / (xy) < y  x
1 / x < 1 / y
2x = 3y First of all if it were realistic GMAT question it would most likely state that \(xy\neq{0}\) and \(x\neq{y}\) (as x, y and xy are in denominators). Is \(\frac{1}{xy}<yx\)? > is \(\frac{1}{xy}+xy<0\) > is \(\frac{1+(xy)^2}{xy}<0\)? as the nominator (\(1+(xy)^2\)) is always positive then the question basically becomes whether denominator (\(xy\)) is negative > is \(xy<0\)? or is \(x<y\)? (1) \(\frac{1}{x}<\frac{1}{y}\) > if both unknowns are positive or both unknowns are negative then \(y<x\) (if both are positive cross multiply to get \(y<x\) and if both are negative cross multiply and flip the sigh twice to get \(y<x\) again) and the answer will be NO but if \(x<0<y\) given inequality also holds true and in this case the answer will be YES (if \(x\) is any negative number and \(y\) is any positive number then \(\frac{1}{x}=negative<positive=\frac{1}{y}\)). Not sufficient. (2) \(2x=3y\) > \(x\) and \(y\) have the same sign, next: \(\frac{x}{y}=\frac{3}{2}\): if both \(x\) and \(y\) are positive (for example 3 and 2 respectively) then \(0<y<x\) and the answer will be NO but if both \(x\) and \(y\) are negative (for example 3 and 2 respectively) then \(x<y<0\) and the answer will be NO. Not sufficient. (1)+(2) As from (2) \(x\) and \(y\) have the same sign then from (1) \(y<x\) and the answer to the question is NO. Sufficient. Answer: C. Hello Bunuel, Agree with your approach but I wanted to plug in nos and check so here it goes. we get the expression ( 1+ (xy)^2 )/(xy) <0> Q becomes Is x<y ? From St 1, we get 1/x<1/y > 1/x1/y <0 and therefore expression becomes (yx)/xy < 0 which means is y<x Now lets take values y=2 , x=3, the expression is true i.e <0 y=2 and x=3, the expression is false ie >0 So not sufficient from St 2, we get x= 3/2y Now y=4, x=6, Expression is False ie >0 y=4, x=6, expression is true i.e <0 So alone not sufficient Now Combining we get y<x and x=3/2y > y< 3/2y which means Y > 0 and x>y. So we have x>y>0. For this condition, the expression is always false ie. ( 1+ (xy)^2 )/(xy) >0 Can't thank you enough in solving inequalities the way you just did. Thanks Mridul
_________________
“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.”



Math Expert
Joined: 02 Sep 2009
Posts: 39753

Re: Is 1/(xy) < y  x [#permalink]
Show Tags
15 Jul 2013, 00:44



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16024

Re: Is 1/(xy) < y  x [#permalink]
Show Tags
07 Aug 2014, 22:46
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Senior Manager
Joined: 08 Apr 2012
Posts: 453

Re: Is 1/(xy) < y  x [#permalink]
Show Tags
15 Sep 2014, 13:54
Bunuel wrote: rxs0005 wrote: Is 1 / (xy) < y  x
1 / x < 1 / y
2x = 3y First of all if it were realistic GMAT question it would most likely state that \(xy\neq{0}\) and \(x\neq{y}\) (as x, y and xy are in denominators). Is \(\frac{1}{xy}<yx\)? > is \(\frac{1}{xy}+xy<0\) > is \(\frac{1+(xy)^2}{xy}<0\)? as the nominator (\(1+(xy)^2\)) is always positive then the question basically becomes whether denominator (\(xy\)) is negative > is \(xy<0\)? or is \(x<y\)? (1) \(\frac{1}{x}<\frac{1}{y}\) > if both unknowns are positive or both unknowns are negative then \(y<x\) (if both are positive cross multiply to get \(y<x\) and if both are negative cross multiply and flip the sigh twice to get \(y<x\) again) and the answer will be NO but if \(x<0<y\) given inequality also holds true and in this case the answer will be YES (if \(x\) is any negative number and \(y\) is any positive number then \(\frac{1}{x}=negative<positive=\frac{1}{y}\)). Not sufficient. (2) \(2x=3y\) > \(x\) and \(y\) have the same sign, next: \(\frac{x}{y}=\frac{3}{2}\): if both \(x\) and \(y\) are positive (for example 3 and 2 respectively) then \(0<y<x\) and the answer will be NO but if both \(x\) and \(y\) are negative (for example 3 and 2 respectively) then \(x<y<0\) and the answer will be NO. Not sufficient. (1)+(2) As from (2) \(x\) and \(y\) have the same sign then from (1) \(y<x\) and the answer to the question is NO. Sufficient. Answer: C. Hi Bunuel. When taking both statements together, I substituted x=3/2 and y=2/3, or x=3/2 and y=2/3 When taking into account statement 1, I noticed that we can't have the negative value for the numbers, as then statement 1 won't hold true. Is this true? Am I missing something?



Math Expert
Joined: 02 Sep 2009
Posts: 39753

Re: Is 1/(xy) < y  x [#permalink]
Show Tags
15 Sep 2014, 21:00
ronr34 wrote: Bunuel wrote: rxs0005 wrote: Is 1 / (xy) < y  x
1 / x < 1 / y
2x = 3y First of all if it were realistic GMAT question it would most likely state that \(xy\neq{0}\) and \(x\neq{y}\) (as x, y and xy are in denominators). Is \(\frac{1}{xy}<yx\)? > is \(\frac{1}{xy}+xy<0\) > is \(\frac{1+(xy)^2}{xy}<0\)? as the nominator (\(1+(xy)^2\)) is always positive then the question basically becomes whether denominator (\(xy\)) is negative > is \(xy<0\)? or is \(x<y\)? (1) \(\frac{1}{x}<\frac{1}{y}\) > if both unknowns are positive or both unknowns are negative then \(y<x\) (if both are positive cross multiply to get \(y<x\) and if both are negative cross multiply and flip the sigh twice to get \(y<x\) again) and the answer will be NO but if \(x<0<y\) given inequality also holds true and in this case the answer will be YES (if \(x\) is any negative number and \(y\) is any positive number then \(\frac{1}{x}=negative<positive=\frac{1}{y}\)). Not sufficient. (2) \(2x=3y\) > \(x\) and \(y\) have the same sign, next: \(\frac{x}{y}=\frac{3}{2}\): if both \(x\) and \(y\) are positive (for example 3 and 2 respectively) then \(0<y<x\) and the answer will be NO but if both \(x\) and \(y\) are negative (for example 3 and 2 respectively) then \(x<y<0\) and the answer will be NO. Not sufficient. (1)+(2) As from (2) \(x\) and \(y\) have the same sign then from (1) \(y<x\) and the answer to the question is NO. Sufficient. Answer: C. Hi Bunuel. When taking both statements together, I substituted x=3/2 and y=2/3, or x=3/2 and y=2/3 When taking into account statement 1, I noticed that we can't have the negative value for the numbers, as then statement 1 won't hold true. Is this true? Am I missing something? Yes, when we combine the statements we get that x > y and 2x = 3y, so x > y > 0.
_________________
New to the Math Forum? Please read this: 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



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16024

Re: Is 1/(xy) < y  x [#permalink]
Show Tags
07 Oct 2015, 04:27
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Manager
Status: tough ... ? Naaahhh !!!!
Joined: 08 Sep 2015
Posts: 67
Location: India
Concentration: Marketing, Strategy
WE: Marketing (Computer Hardware)

Re: Is 1/(xy) < y  x [#permalink]
Show Tags
07 Oct 2015, 05:33
Hi All, I attended this question quite late from the posting date but i am getting the different answer D.
1) 1/x<1/y  which means x>y..so for the positive values the given expression holds NO, and for the negaive values X=1 and Y=2 (X>Y) the expression says NO.
2) 2x=3y  which means x>y..so the same solution like above
So both gives the answer.
Can you help.



Math Expert
Joined: 02 Sep 2009
Posts: 39753

Re: Is 1/(xy) < y  x [#permalink]
Show Tags
07 Oct 2015, 05:44



Math Forum Moderator
Joined: 20 Mar 2014
Posts: 2647
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: Is 1/(xy) < y  x [#permalink]
Show Tags
07 Oct 2015, 05:46
asethi wrote: Hi All, I attended this question quite late from the posting date but i am getting the different answer D.
1) 1/x<1/y  which means x>y..so for the positive values the given expression holds NO, and for the negaive values X=1 and Y=2 (X>Y) the expression says NO.
2) 2x=3y  which means x>y..so the same solution like above
So both gives the answer.
Can you help. Be very careful with multiplying or diving inequalities with variables for which you do not know the signs of. In this case as well, you do not know whether x and y are both positive or both negative or one negative one positive etc. Without this information you can not say x>y when you are given 1/x<1/y Case in point, consider the cases (3,2) and (2,3) you get different answers and because of this the first statement is not sufficient. You are making the same mistake when you are analyzing statement 2 alone. Make sure to be extra careful when dealing with unknown variables in inequalities. Hope this helps.
_________________
Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidatedthursdaywithronlistforallthesections201006.html#p1544515 Rules for Posting in Quant Forums: http://gmatclub.com/forum/rulesforpostingpleasereadthisbeforeposting133935.html Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rulesforpostingpleasereadthisbeforeposting133935.html#p1096628 GMATCLUB Math Book: http://gmatclub.com/forum/gmatmathbookindownloadablepdfformat130609.html Everything Related to Inequalities: http://gmatclub.com/forum/inequalitiesmadeeasy206653.html#p1582891 Inequalities tips: http://gmatclub.com/forum/inequalitiestipsandhints175001.html Debrief, 650 to 750: http://gmatclub.com/forum/650to750a10monthjourneytothescore203190.html



Intern
Joined: 17 May 2013
Posts: 21
Location: India
GPA: 3.26

Is 1/(xy) < y  x [#permalink]
Show Tags
16 Apr 2016, 04:23
1
This post received KUDOS
Bunuel wrote: rxs0005 wrote: Is 1 / (xy) < y  x
1 / x < 1 / y
2x = 3y First of all if it were realistic GMAT question it would most likely state that \(xy\neq{0}\) and \(x\neq{y}\) (as x, y and xy are in denominators). Is \(\frac{1}{xy}<yx\)? > is \(\frac{1}{xy}+xy<0\) > is \(\frac{1+(xy)^2}{xy}<0\)? as the nominator (\(1+(xy)^2\)) is always positive then the question basically becomes whether denominator (\(xy\)) is negative > is \(xy<0\)? or is \(x<y\)? (1) \(\frac{1}{x}<\frac{1}{y}\) > if both unknowns are positive or both unknowns are negative then \(y<x\) (if both are positive cross multiply to get \(y<x\) and if both are negative cross multiply and flip the sigh twice to get \(y<x\) again) and the answer will be NO but if \(x<0<y\) given inequality also holds true and in this case the answer will be YES (if \(x\) is any negative number and \(y\) is any positive number then \(\frac{1}{x}=negative<positive=\frac{1}{y}\)). Not sufficient. (2) \(2x=3y\) > \(x\) and \(y\) have the same sign, next: \(\frac{x}{y}=\frac{3}{2}\): if both \(x\) and \(y\) are positive (for example 3 and 2 respectively) then \(0<y<x\) and the answer will be NO but if both \(x\) and \(y\) are negative (for example 3 and 2 respectively) then \(x<y<0\) and the answer will be NO. Not sufficient. (1)+(2) As from (2) \(x\) and \(y\) have the same sign then from (1) \(y<x\) and the answer to the question is NO. Sufficient. Answer: C. Bunuel, you might want to change the NO in red, which is almost at the bottom, to 'YES'.




Is 1/(xy) < y  x
[#permalink]
16 Apr 2016, 04:23



Go to page
1 2
Next
[ 22 posts ]




