Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 25 Jul 2010
Posts: 132

If x and y are integers and x > 0, is y > 0? [#permalink]
Show Tags
11 Sep 2010, 15:05
1
This post received KUDOS
8
This post was BOOKMARKED
Question Stats:
61% (01:25) correct 39% (01:11) wrong based on 347 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.
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: 44423

Re: If x and y are integers and x > 0, is y > 0? [#permalink]
Show Tags
11 Sep 2010, 15:17
3
This post received KUDOS
Expert's post
2
This post was BOOKMARKED
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: 132

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: 246

Re: If x and y are integers and x > 0, is y > 0? [#permalink]
Show Tags
11 Sep 2010, 15:34
1
This post received KUDOS
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: 44423

Re: If x and y are integers and x > 0, is y > 0? [#permalink]
Show Tags
11 Sep 2010, 15:39
2
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
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: 132

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: 30

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: 44423

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: 682
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: 2754
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.



Intern
Joined: 16 Apr 2017
Posts: 16

Re: If x and y are integers and x > 0, is y > 0? [#permalink]
Show Tags
19 Oct 2017, 12:10
Bunuel , could you illustrate the graphical solution for this problem too? The graph of the first statement passes through the origin and lies to the right of the line in the 1st quadrant and to its left in the third quadrant. If x is positive, only values in the first quadrant hold. Then y>0, is it not? OA a?




Re: If x and y are integers and x > 0, is y > 0?
[#permalink]
19 Oct 2017, 12:10






