Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 25 Jul 2010
Posts: 124

If x and y are integers and x > 0, is y > 0?
[#permalink]
Show Tags
Updated on: 27 Jul 2017, 06:07
Question Stats:
62% (01:25) correct 38% (01:11) wrong based on 356 sessions
HideShow timer Statistics
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?
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by Orange08 on 11 Sep 2010, 15:05.
Last edited by mvictor on 27 Jul 2017, 06:07, edited 1 time in total.
included author's explanations in a spoiler




Math Expert
Joined: 02 Sep 2009
Posts: 47112

Re: If x and y are integers and x > 0, is y > 0?
[#permalink]
Show Tags
11 Sep 2010, 15:17
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.
_________________
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: 25 Jul 2010
Posts: 124

Re: If x and y are integers and x > 0, is y > 0?
[#permalink]
Show Tags
11 Sep 2010, 15:26
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?



Manager
Joined: 20 Jul 2010
Posts: 230

Re: If x and y are integers and x > 0, is y > 0?
[#permalink]
Show Tags
11 Sep 2010, 15:34
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 AB>0. A=2, B 5 will prove this.
_________________
If you like my post, consider giving me some KUDOS !!!!! Like you I need them



Math Expert
Joined: 02 Sep 2009
Posts: 47112

Re: If x and y are integers and x > 0, is y > 0?
[#permalink]
Show Tags
11 Sep 2010, 15:39
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 \(<\)) > \(ac>bd\) (take the sign of the inequality you subtract from). Example: \(3<4\) and \(5>1\) > \(35<41\). So we can only add \(7x  2y > 0\) and \(7x + 7y > 0\) as their signs are in the same direction (>). Hope it helps.
_________________
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: 25 Jul 2010
Posts: 124

Re: If x and y are integers and x > 0, is y > 0?
[#permalink]
Show Tags
12 Sep 2010, 01:37
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 \(<\)) > \(ac>bd\) (take the sign of the inequality you subtract from). Example: \(3<4\) and \(5>1\) > \(35<41\).
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.



Intern
Joined: 14 Jul 2013
Posts: 25

Re: If x and y are integers and x > 0, is y > 0?
[#permalink]
Show Tags
03 May 2014, 21:22
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.



Math Expert
Joined: 02 Sep 2009
Posts: 47112

Re: If x and y are integers and x > 0, is y > 0?
[#permalink]
Show Tags
04 May 2014, 03:09



Director
Joined: 26 Oct 2016
Posts: 664
Location: United States
Concentration: Marketing, International Business
GPA: 4
WE: Education (Education)

Re: If x and y are integers and x > 0, is y > 0?
[#permalink]
Show Tags
11 Feb 2017, 01:17
1) 7x2y>0 7(8)2(3) = positive 7(8)2(3) = positive y can be neg or pos. NOT sufficient. 2) y<x x = 8 , y can equal 3 x = 8, 3<8, so y can be positive x = 8, y can equal 3 x=8, (3)<8, 6<8, y can be negative too. Not sufficient. c) combined: Look at the breakdown from statement (1) with numbers that also satisfy statement (2)'s criteria. y can be neg OR positive. Answer is Choice E.
_________________
Thanks & Regards, Anaira Mitch



Board of Directors
Joined: 17 Jul 2014
Posts: 2723
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: If x and y are integers and x > 0, is y > 0?
[#permalink]
Show Tags
27 Jul 2017, 06:11
from 1 alone y can be negative and y can be positive say y=1 and x=1. 7+2=9. 9>0
say y=1 and x=1 72=5. 5>0
1 alone is insufficient. A and D are out.
statement 2 says y<x. rewrite 0<x+y y can be negative and y can be positive. say y=1 and x=2 21 = 1. 1>0. works
say y=1 and x=1 1+1=2. 2>0. works.
B is out, so we are left with either C or E  50/50 chance we'd get it right, not bad but combining, we see that both statements say that y can be > or < 0. C is out, and E is the answer.




Re: If x and y are integers and x > 0, is y > 0? &nbs
[#permalink]
27 Jul 2017, 06:11






