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Is xy > x/y?

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Is xy > x/y? [#permalink] New post 28 May 2014, 08:00
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Is xy > x/y?

(1) 0 < y < 1

(2) xy > 1

[Reveal] Spoiler:
Bunnel could you please look into this.

official ans is C. but i am getting A

Last edited by Bunuel on 28 May 2014, 08:51, edited 1 time in total.
Edited the question.
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Re: Is xy>xy? [#permalink] New post 28 May 2014, 08:50
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PathFinder007 wrote:
Is xy>xy?
(1) 0<y<1

(2) xy>1

Bunnel could you please look into this.

official ans is C. but i am getting A


I guess you are talking about question m18 q30.

Is xy>\frac{x}{y}?

Is xy>\frac{x}{y}? --> is x(y-\frac{1}{y})>0?

(1) 0<y<1. From this statement it follows that (y-\frac{1}{y})<0. Now, if x>0 then x(y-\frac{1}{y})<0 but if x<0 then x(y-\frac{1}{y})>0. Not sufficient.

(2) xy>1. If x=y=2 then the answer is YES but if x=4 and y=\frac{1}{2} then the answer is NO. Not sufficient.

(1)+(2) Since from (1) y>0 and from (2) xy>1 then x>0. So, we have that x>0 and (y-\frac{1}{y})<0 (from 1), which means that their product x(y-\frac{1}{y})<0. Sufficient.

Answer: C.
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Re: Is xy>xy? [#permalink] New post 29 May 2014, 10:03
Bunuel wrote:
PathFinder007 wrote:
Is xy>xy?
(1) 0<y<1

(2) xy>1

Bunnel could you please look into this.

official ans is C. but i am getting A


I guess you are talking about question m18 q30.

Is xy>\frac{x}{y}?

Is xy>\frac{x}{y}? --> is x(y-\frac{1}{y})>0?

(1) 0<y<1. From this statement it follows that (y-\frac{1}{y})<0. Now, if x>0 then x(y-\frac{1}{y})<0 but if x<0 then x(y-\frac{1}{y})>0. Not sufficient.

(2) xy>1. If x=y=2 then the answer is YES but if x=4 and y=\frac{1}{2} then the answer is NO. Not sufficient.

(1)+(2) Since from (1) y>0 and from (2) xy>1 then x>0. So, we have that x>0 and (y-\frac{1}{y})<0 (from 1), which means that their product x(y-\frac{1}{y})<0. Sufficient.

Answer: C.




Bunuel,

How come 0<y<1 leads to (y-1/y)<0 ? Isn't it (1-1/y)<0 ?

Regards,
Ammu
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Re: Is xy>xy? [#permalink] New post 29 May 2014, 10:19
Expert's post
ammuseeru wrote:
Bunuel wrote:
PathFinder007 wrote:
Is xy>xy?
(1) 0<y<1

(2) xy>1

Bunnel could you please look into this.

official ans is C. but i am getting A


I guess you are talking about question m18 q30.

Is xy>\frac{x}{y}?

Is xy>\frac{x}{y}? --> is x(y-\frac{1}{y})>0?

(1) 0<y<1. From this statement it follows that (y-\frac{1}{y})<0. Now, if x>0 then x(y-\frac{1}{y})<0 but if x<0 then x(y-\frac{1}{y})>0. Not sufficient.

(2) xy>1. If x=y=2 then the answer is YES but if x=4 and y=\frac{1}{2} then the answer is NO. Not sufficient.

(1)+(2) Since from (1) y>0 and from (2) xy>1 then x>0. So, we have that x>0 and (y-\frac{1}{y})<0 (from 1), which means that their product x(y-\frac{1}{y})<0. Sufficient.

Answer: C.




Bunuel,

How come 0<y<1 leads to (y-1/y)<0 ? Isn't it (1-1/y)<0 ?

Regards,
Ammu


0<y<1, so y is some fraction between 0 and 1. In this case y<1/y, isn't it? For example, say y=1/2, then 1/y=2 --> y<1/y --> (y-1/y)<0.

Does this make sense?
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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.


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Re: Is xy > x/y? [#permalink] New post 11 Aug 2014, 16:42
Bonuel,

What's wrong in my reasoning?

Q) xy > x/y ? ---- reasoning: first thing I notice is the trap related to the Y sign. If Y is positive, I may pass Y to the left side.. but if Y is negative, I cannot do this).

(1) 0 < y < 1 ---- reasoning: so Y is positive, the question becomes is XY.Y > X, or X(Y^2)>X? Then I divide both sides by X, then the question becomes: is Y^2 > 1? Since Y is a fraction (because is greater than 0 but less than 1), I can assume that the square of Y will yield a number below 1, so I can answer the question with a "NO". Stat. A is sufficient

What I did wrong?

Thank you so much!
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Re: Is xy > x/y? [#permalink] New post 12 Aug 2014, 01:14
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rodrigocani wrote:
Bonuel,

What's wrong in my reasoning?

Q) xy > x/y ? ---- reasoning: first thing I notice is the trap related to the Y sign. If Y is positive, I may pass Y to the left side.. but if Y is negative, I cannot do this).

(1) 0 < y < 1 ---- reasoning: so Y is positive, the question becomes is XY.Y > X, or X(Y^2)>X? Then I divide both sides by X, then the question becomes: is Y^2 > 1? Since Y is a fraction (because is greater than 0 but less than 1), I can assume that the square of Y will yield a number below 1, so I can answer the question with a "NO". Stat. A is sufficient

What I did wrong?

Thank you so much!


You cannot divide xy^2 > x by x because you don't know the sign of x. If x is positive then yes, y^2 > 1 but if x is negative, then when dividing by it you should flip the sign and you get y^2 < 1.

Never multiply (or reduce) an inequality by a variable (or the expression with a variable) if you don't know its.

Other tips on Inequalities are here: inequalities-tips-and-hints-175001.html
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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.


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Is xy > x/y? [#permalink] New post 13 Aug 2014, 07:16
In this case, we can see:
(1) doesn't mean anything of x --> (1) is insufficent
(2) xy>1.
_ this case is too risky ( when x = 1 and y = 2 --> xy = 2 but x/y = 1/2, contrastly, x = 3 and y =2 --> xy=6 and x/y = 3/2 = 1,5 )
In combination of 2 cases, xy>1 and 0<y<1, we easily see that x must be superior than 1. When x>1 and 0<y<1, x/y is always bigger than xy. Example: 3*0,5= 4,5 but 3/0,5 = 6
So the answer is C !
Is xy > x/y?   [#permalink] 13 Aug 2014, 07:16
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