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Is xy > 0? [#permalink] New post 16 Nov 2009, 13:27
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Is xy > 0?

(1) x - y > -2
(2) x - 2y < -6
[Reveal] Spoiler: OA
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Re: gmat prep inequalities [#permalink] New post 16 Nov 2009, 13:58
study wrote:
is xy > 0?

1) x - y > -2
2) x - 2y < -6


1) x + 2 > y
If y is +ve, x still could be +ve or -ve.
If x is +ve, y still could be +ve or -ve.

2) x +6 < 2y
x and y could be anything.

1+2 togather:
1) -x - 2 < - y
2) x +6 < 2y

Add up them
-x - 2 < - y
x +6 < 2y
4 < y

We know y is +ve and > 4. x is also +ve.

Suff. C.
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Re: gmat prep inequalities [#permalink] New post 16 Nov 2009, 14:16
Expert's post
study wrote:
is xy > 0?

1) x - y > -2
2) x - 2y < -6


Question basically asks whether x and y have the same sign.

(1) y<x+2, can we find the pair of x and y with different signs satisfying the inequality given? Sure x=1 y any negative value. Can we find the pair of x and y with the same sign satisfying the inequality given? Sure x=5 y=1. So not sufficient to conclude whether x and y have the same sign or not.

(2) y>x/2+6. The same here. We can find x and y with different signs, as well as the same sign to satisfy inequality given. Not sufficient.

(1)+(2) Remember we can subtract inequalities with the signs in different direction. (1)-(2) 0<x/2-4 --> 8<x. So we get that x is positive and we know from (2) that y>x/2+6. x/2+6 is some positive value and y is more than that positive value, or in another words y is positive too. Sufficient.

Answer: C.

The problem above can be solved in different way:
(1) y<x+2 represent all x,y points which are below the line y=x+2. If you draw this line you'll see that this are consists of the points which are in all quadrants. Or there are xy points with all combinations of x and y: positive x negative y, positive x positive y etc. and we are looking whether x and y are eother from the I quadrant or from the III. Not sufficient.

(2) y>x/2+6. Again if you draw the line y=x/2+6, the points satisfying the inequality given would be above of this line. The points would be in quadrants I, II, or III. Not sufficient.

(1)+(2) The area you'll receive from the two inequalities y<x+2 and y>x/2+6 (below the first and above the second line) will be consisting from the points which are only I quadrant, which means that x and y are both positive. Hence xy is positive. Sufficient.

Answer: C.
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Re: gmat prep inequalities [#permalink] New post 16 Nov 2009, 14:24
Bunuel wrote:
study wrote:
is xy > 0?

1) x - y > -2
2) x - 2y < -6


Question basically asks whether x and y have the same sign.

(1) y<x+2, can we find the pair of x and y with different signs satisfying the inequality given? Sure x=1 y any negative value. Can we find the pair of x and y with the same sign satisfying the inequality given? Sure x=5 y=1. So not sufficient to conclude whether x and y have the same sign or not.

(2) y>x/2+6. The same here. We can find x and y with different signs, as well as the same sign to satisfy inequality given. Not sufficient.

(1)+(2) Remember we can subtract inequalities with the signs in different direction. (1)-(2) 0<x/2-4 --> 8<x. So we get that x is positive and we know from (2) that y>x/2+6. x/2+6 is some positive value and y is more than that positive value, or in another words y is positive too. Sufficient.

Answer: C.

The problem above can be solved in different way:
(1) y<x+2 represent all x,y points which are below the line y=x+2. If you draw this line you'll see that this are consists of the points which are in all quadrants. Or there are xy points with all combinations of x and y: positive x negative y, positive x positive y etc. and we are looking whether x and y are eother from the I quadrant or from the III. Not sufficient.

(2) y>x/2+6. Again if you draw the line y=x/2+6, the points satisfying the inequality given would be above of this line. The points would be in quadrants I, II, or III. Not sufficient.

(1)+(2) The area you'll receive from the two inequalities y<x+2 and y>x/2+6 (below the first and above the second line) will be consisting from the points which are only I quadrant, which means that x and y are both positive. Hence xy is positive. Sufficient.

Answer: C.


as a review..subtract with signs in different directions and add with signs in same direction?
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Re: gmat prep inequalities [#permalink] New post 16 Nov 2009, 14:35
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Expert's post
lagomez wrote:
as a review..subtract with signs in different directions and add with signs in same direction?


Yes.

You can only add inequalities when their signs are in the same direction.

You can only apply subtraction when their signs are in the opposite directions.
_________________

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: gmat prep inequalities [#permalink] New post 16 Nov 2009, 20:48
Bunuel wrote:
lagomez wrote:
as a review..subtract with signs in different directions and add with signs in same direction?


Yes.

You can only add inequalities when their signs are in the same direction.

You can only apply subtraction when their signs are in the opposite directions.


Bunuel, can you give examples along to make this more clear?

Which sign would the final inequalities take when you subtract them?

Thanks in advance
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Re: gmat prep inequalities [#permalink] New post 17 Nov 2009, 04:46
Expert's post
lonewolf wrote:
Bunuel, can you give examples along to make this more clear?

Which sign would the final inequalities take when you subtract them?

Thanks in advance


1. a>b and 2. c<d --> a-c>b-d, so the sign > of the 1. (the sign of the one you subtracting from).

You can look at this in another way: c<d means -c>-d, now add inequalities a-c>b-d.

eg. 5>3 and 2<7 --> 5-2>3-7, 3>-4.

Hope it's clear.
_________________

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.


What are GMAT Club Tests?
25 extra-hard Quant Tests

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Re: gmat prep inequalities [#permalink] New post 17 Nov 2009, 05:09
Bunuel wrote:
lonewolf wrote:
Bunuel, can you give examples along to make this more clear?

Which sign would the final inequalities take when you subtract them?

Thanks in advance


1. a>b and 2. c<d --> a-c>b-d, so the sign > of the 1. (the sign of the one you subtracting from).

You can look at this in another way: c<d means -c>-d, now add inequalities a-c>b-d.

eg. 5>3 and 2<7 --> 5-2>3-7, 3>-4.

Hope it's clear.


Great! Crystal Clear
Re: gmat prep inequalities   [#permalink] 17 Nov 2009, 05:09
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