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If x and y are integers and x > 0, is y > 0?

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If x and y are integers and x > 0, is y > 0? [#permalink] New post 11 Sep 2010, 14:05
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E

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67% (02:04) correct 33% (00:44) wrong based on 83 sessions
If x and y are integers and x > 0, is y > 0?

(1) 7x – 2y > 0
(2) -y < x


From 1, y can have +ve and -ve values. For example, x = 2, y = 1 or x = 2, y = -1. Thus, not sufficient to answer whether y >0

From 2, -y < x or x +y > 0, again not sufficient. x = 0.9, y = -0.8 or x = 0.9, y = 0.8

Combining 1 & 2
7x - 2y > 0
x + y > 0

----------------

7x - 2y > 0
7x + 7y > 0 (multiplying earlier equation 2 by 7)

summing the above two equations, can't we derive 5y > 0 and thus y > 0?
[Reveal] Spoiler: OA
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Re: Is y > 0? [#permalink] New post 11 Sep 2010, 14:17
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Orange08 wrote:
If x and y are integers and x > 0, is y > 0?
(1) 7x – 2y > 0
(2) -y < x


From 1, y can have +ve and -ve values. For example, x = 2, y = 1 or x = 2, y = -1. Thus, not sufficient to answer whether y >0

From 2, -y < x or x +y > 0, again not sufficient. x = 0.9, y = -0.8 or x = 0.9, y = 0.8

Combining 1 & 2
7x - 2y > 0
x + y > 0

----------------

7x - 2y > 0
7x + 7y > 0 (multiplying earlier equation 2 by 7)

summing the above two equations, can't we derive 5y > 0 and thus y > 0?


If y=0 and x is any positive integer both statements hold true and the answer to the question is NO.
If y=1 and x=2 again both statements hold true and the answer to the question is YES.
Two different answers. Not sufficient.

Answer: E.

As for your question: when we sum 7x - 2y > 0 and 7x + 7y > 0 we'll get 14x+5y>0 and not 5y > 0.

Hope it helps.
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Re: Is y > 0? [#permalink] New post 11 Sep 2010, 14:26
Bunuel wrote:
Orange08 wrote:
x + y > 0

----------------

As for your question: when we sum 7x - 2y > 0 and 7x + 7y > 0 we'll get 14x+5y>0 and not 5y > 0.

Hope it helps.

Thanks. Oh ya,, silly mistake from me. I meant subtracting equation 2 from 1 will lead us to
9y >0 and eventually y > 0.

Am i wrong in performing such subtractions for inequalities?
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Re: Is y > 0? [#permalink] New post 11 Sep 2010, 14:34
Orange08 wrote:
Bunuel wrote:
Orange08 wrote:
x + y > 0

----------------

As for your question: when we sum 7x - 2y > 0 and 7x + 7y > 0 we'll get 14x+5y>0 and not 5y > 0.

Hope it helps.

Thanks. Oh ya,, silly mistake from me. I meant subtracting equation 2 from 1 will lead us to
9y >0 and eventually y > 0.

Am i wrong in performing such subtractions for inequalities?


I don't think simultaneous equations are solved on inequalities.

If A > 0 and B> 0; it doesn't mean A-B>0. A=2, B 5 will prove this.
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Re: Is y > 0? [#permalink] New post 11 Sep 2010, 14:39
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Orange08 wrote:
Bunuel wrote:
Orange08 wrote:
x + y > 0

----------------

As for your question: when we sum 7x - 2y > 0 and 7x + 7y > 0 we'll get 14x+5y>0 and not 5y > 0.

Hope it helps.

Thanks. Oh ya,, silly mistake from me. I meant subtracting equation 2 from 1 will lead us to
9y >0 and eventually y > 0.

Am i wrong in performing such subtractions for inequalities?


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

If a>b and c>d (signs in same direction: > and >) --> a+c>b+d.
Example: 3<4 and 2<5 --> 3+2<4+5.

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

If a>b and c<d (signs in opposite direction: > and <) --> a-c>b-d (take the sign of the inequality you subtract from).
Example: 3<4 and 5>1 --> 3-5<4-1.

So we can only add 7x - 2y > 0 and 7x + 7y > 0 as their signs are in the same direction (>).

Hope it helps.
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Re: Is y > 0? [#permalink] New post 11 Sep 2010, 15:57
Nice. I didn't think this for inequalities.
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Re: Is y > 0? [#permalink] New post 12 Sep 2010, 00:37
Bunuel wrote:

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

If a>b and c>d (signs in same direction: > and >) --> a+c>b+d.
Example: 3<4 and 2<5 --> 3+2<4+5.

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

If a>b and c<d (signs in opposite direction: > and <) --> a-c>b-d (take the sign of the inequality you subtract from).
Example: 3<4 and 5>1 --> 3-5<4-1.

So we can only add 7x - 2y > 0 and 7x + 7y > 0 as their signs are in the same direction (>).

Hope it helps.


Absolutely fantastic. Thanks Bunuel once again. This has indeed cleared one of the flaws in my understanding.
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in [#permalink] New post 08 Feb 2012, 23:42
According to my doc, the OA is E.
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Re: If x and y are integers and x > 0; is y > 0 ? (1) 7x - [#permalink] New post 09 Feb 2012, 00:12
The answer is definitely E.
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Re: If x and y are integers and x > 0, is y > 0? [#permalink] New post 15 Oct 2013, 01:29
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Re: If x and y are integers and x > 0, is y > 0? [#permalink] New post 03 May 2014, 20:22
If x and y are integers and x > 0, is y > 0?

(1) 7x – 2y > 0
(2) -y < x


Bunuel, please have a look at this.

statement1. 7x - 2y > 0
=> x > 2y/7---------(1)

y can be negative or positive. Not sufficient

statement2. -y < x
=> x + y > 0---------(2)

Again, y can be negative or positive. Not Sufficient.

statement 1 & 2 Together.

from eq. (1) & (2),
[a value > 2y/7] + y > 0
lets consider least value of x (actually this would be lesser than the least).
2y/7 + y > 0
=> 9y/7 > 0 or (9/7)y>0
therefore, y must be > than 0.

Answer C.
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Re: If x and y are integers and x > 0, is y > 0? [#permalink] New post 04 May 2014, 02:09
Expert's post
honey86 wrote:
If x and y are integers and x > 0, is y > 0?

(1) 7x – 2y > 0
(2) -y < x


Bunuel, please have a look at this.

statement1. 7x - 2y > 0
=> x > 2y/7---------(1)

y can be negative or positive. Not sufficient

statement2. -y < x
=> x + y > 0---------(2)

Again, y can be negative or positive. Not Sufficient.

statement 1 & 2 Together.

from eq. (1) & (2),
[a value > 2y/7] + y > 0
lets consider least value of x (actually this would be lesser than the least).
2y/7 + y > 0
=> 9y/7 > 0 or (9/7)y>0
therefore, y must be > than 0.

Answer C.


Why are you considering the least value of x??? Nothing prevents x to be greater than this value and in this case your logic will not hold.
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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: If x and y are integers and x > 0, is y > 0?   [#permalink] 04 May 2014, 02:09
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