November 20, 2018 November 20, 2018 09:00 AM PST 10:00 AM PST The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat. November 20, 2018 November 20, 2018 06:00 PM EST 07:00 PM EST What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50627

If x  + y  = x – y and xy does not equal 0, which of the followin
[#permalink]
Show Tags
15 Oct 2014, 15:42
Question Stats:
74% (01:02) correct 26% (01:28) wrong based on 1109 sessions
HideShow timer Statistics




Math Expert
Joined: 02 Sep 2009
Posts: 50627

Re: If x  + y  = x – y and xy does not equal 0, which of the followin
[#permalink]
Show Tags
02 Jan 2015, 04:26
saadis87 wrote: WoundedTiger wrote: Bunuel wrote: Tough and Tricky questions: Absolute Values. If x  + y  = x – y and xy does not equal 0, which of the following must be true? A. x + y > 0 B. x + y < 0 C. x – y > 0 D. x – y < 0 E. x^2 – y^2 > 0 Good question: 20 sec solution We know that for any \(x\geq{0}\) We are told that \(xy \neq{0}\)that means neither x nor y is 0 Now in LHS we have x+y, which is greater than 0 So we have x+y> 0 or \(xy >0\) or (x+y)>0 or\(x+y<0\) Ans B Isnt the rule x>0 when x is positive and x<0 when X is negative (I know im mistaken, but I dont know where so please do point out ) so shouldn't (x+y)<0 No. The absolute value of some expression is always nonnegative: \(some \ expression\geq{0}\), no matter whether that expression itself is positive, negative or 0. When \(x \le 0\) then \(x=x\), or more generally when \(\text{some expression} \le 0\) then \(\text{some expression} = (\text{some expression})\). For example: \(5=5=(5)\); When \(x \ge 0\) then \(x=x\), or more generally when \(\text{some expression} \ge 0\) then \(\text{some expression} = \text{some expression}\). For example: \(5=5\). 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




Director
Joined: 25 Apr 2012
Posts: 689
Location: India
GPA: 3.21
WE: Business Development (Other)

Re: If x  + y  = x – y and xy does not equal 0, which of the followin
[#permalink]
Show Tags
16 Oct 2014, 21:05
Bunuel wrote: Tough and Tricky questions: Absolute Values. If x  + y  = x – y and xy does not equal 0, which of the following must be true? A. x + y > 0 B. x + y < 0 C. x – y > 0 D. x – y < 0 E. x^2 – y^2 > 0 Good question: 20 sec solution We know that for any \(x\geq{0}\) We are told that \(xy \neq{0}\)that means neither x nor y is 0 Now in LHS we have x+y, which is greater than 0 So we have x+y> 0 or \(xy >0\) or (x+y)>0 or\(x+y<0\) Ans B
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”




Intern
Joined: 18 Dec 2013
Posts: 27
Location: Canada
GPA: 2.84
WE: Project Management (Telecommunications)

Re: If x  + y  = x – y and xy does not equal 0, which of the followin
[#permalink]
Show Tags
15 Oct 2014, 19:12
Bunuel wrote: Tough and Tricky questions: Absolute Values. If x  + y  = x – y and xy does not equal 0, which of the following must be true? A. x + y > 0 B. x + y < 0 C. x – y > 0 D. x – y < 0 E. x^2 – y^2 > 0 Took me about 2 mins to complete. Feedback's are welcome, if I have missed or omitted anything from my method
Question stem mentions \(X  + Y = X Y\) > from this you can drive that only possibility to satisfy the equation is when \(X & Y\) both are negative. Example: Assume \(X=2\) and \(Y=1\) Then, substitute in the given equation \(LHS = 2+1 = 2+1\) & \(RHS = (2)(1) = 2+1 = 3\) Therefore, \(LHS = RHS\)
Now, that you know \(X & Y\) both are negative, substitute in each option>
option A: \(X + Y > 0\), therefore, \(ve + ve\) will always be less than zero, hence does not satisfy the equation. option B: \(X+Y < 0\), therefore, \(ve + ve\) will always be less than zero, hence satisfies the equation. option C: \(X  Y > 0\), therefore, \((ve)  (ve)\) can be less than zero or more than zero, hence does not satisfy the equation. option D: \(X  Y < 0\), therefore, \((ve)  (ve)\) can be less than zero or more than zero, hence does not satisfy the equation. option E: \(X^2Y^2 > 0\), therefore, \((ve)^2  (ve)^2 = (+ve)  (+ve)\) can be less than zero or more than zero, hence does not satisfy the equation.
Since only option B Satisfies the equation, the correct answer choice is option B



Manager
Joined: 13 Sep 2014
Posts: 88
WE: Engineering (Consulting)

Re: If x  + y  = x – y and xy does not equal 0, which of the followin
[#permalink]
Show Tags
15 Oct 2014, 19:28
From given equation, it can be easily deduced that x<0, y<0 so (ve) + (ve) = (ve) < 0



Intern
Joined: 09 Jul 2014
Posts: 34

Re: If x  + y  = x – y and xy does not equal 0, which of the followin
[#permalink]
Show Tags
17 Oct 2014, 09:54
If x is <0, then x = x , so From the given equation we can figure out that x and y are both negative numbers . thus, ve + (Ve) will always be <0 hence B. Bunuel please let me know if my approach is wrong !



Intern
Joined: 12 May 2014
Posts: 14
Location: United States
Concentration: Strategy, Operations
GMAT Date: 10222014
GPA: 1.9
WE: Engineering (Energy and Utilities)

Re: If x  + y  = x – y and xy does not equal 0, which of the followin
[#permalink]
Show Tags
18 Oct 2014, 03:15
according to question x+y = xy only when both x and y are negative(<0).. The sum of two negative numbers is negative (<0)...hence B....
kudos:)



Manager
Status: I am not a product of my circumstances. I am a product of my decisions
Joined: 20 Jan 2013
Posts: 118
Location: India
Concentration: Operations, General Management
GPA: 3.92
WE: Operations (Energy and Utilities)

Re: If x  + y  = x – y and xy does not equal 0, which of the followin
[#permalink]
Show Tags
18 Oct 2014, 06:46
Bunuel wrote: Tough and Tricky questions: Absolute Values. If x  + y  = x – y and xy does not equal 0, which of the following must be true? A. x + y > 0 B. x + y < 0 C. x – y > 0 D. x – y < 0 E. x^2 – y^2 > 0 Given that, x  + y  = x – yLHS = x  + y , implies that LHS > 0 {because mod is always +ve }This implies that RHS > 0 i.e. x – y > 0 (X + Y ) > 0 Multiply by 1 on both sides and flip inequality signwe get (X + Y ) < 0. Hence answer is B



Intern
Joined: 13 Dec 2013
Posts: 44
GPA: 2.71

Re: If x  + y  = x – y and xy does not equal 0, which of the followin
[#permalink]
Show Tags
01 Jan 2015, 14:07
WoundedTiger wrote: Bunuel wrote: Tough and Tricky questions: Absolute Values. If x  + y  = x – y and xy does not equal 0, which of the following must be true? A. x + y > 0 B. x + y < 0 C. x – y > 0 D. x – y < 0 E. x^2 – y^2 > 0 Good question: 20 sec solution We know that for any \(x\geq{0}\) We are told that \(xy \neq{0}\)that means neither x nor y is 0 Now in LHS we have x+y, which is greater than 0 So we have x+y> 0 or \(xy >0\) or (x+y)>0 or\(x+y<0\) Ans B Isnt the rule x>0 when x is positive and x<0 when X is negative (I know im mistaken, but I dont know where so please do point out ) so shouldn't (x+y)<0



Director
Joined: 23 Jan 2013
Posts: 569

Re: If x  + y  = x – y and xy does not equal 0, which of the followin
[#permalink]
Show Tags
25 May 2015, 07:22
x + y = xy =>  (x+y)
means that x+y<0 for their negative to be positive
B



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12882
Location: United States (CA)

Re: If x  + y  = x – y and xy does not equal 0, which of the followin
[#permalink]
Show Tags
26 May 2015, 20:59
Hi All, This question can be solved by TESTing VALUES. We're told that X + Y = X Y and that neither variable equals 0. We're asked which of the following answers MUST be true (which really means "which of the following is ALWAYS TRUE no matter how many different examples we come up with....?) As complicated as this might look, it's really just telling us to use NEGATIVE values for X and Y. From the answer choices (and their focus on the relationship to 0), we should look to pick the SAME number for BOTH variables... IF.... X = 1 Y = 1 Answer A: X+Y > 0 1 1 = 2 is NOT > 0. NOT the answer Answer B: X+Y < 0 1  1 = 2 IS < 0. This is a MATCH Answer C: XY > 0 1 +1 = 0 is NOT > 0. NOT the answer Answer D: XY < 0 1 +1 = 0 is NOT < 0. NOT the answer Answer E: X^2 – Y^2 > 0 1  1 = 0 is NOT > 0. NOT the answer Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2203

Re: If x  + y  = x – y and xy does not equal 0, which of the followin
[#permalink]
Show Tags
26 May 2015, 22:38
Bunuel wrote: Tough and Tricky questions: Absolute Values. If x  + y  = x – y and xy does not equal 0, which of the following must be true? A. x + y > 0 B. x + y < 0 C. x – y > 0 D. x – y < 0 E. x^2 – y^2 > 0 Going through the solutions posted above, I realized that while most students did answer the question right, some missed out on an important nuance: It is incorrect to say that an absolute value expression is always positive.The correct statement is: An absolute value expression is always nonnegative.This means, x ≥ 0 (please note that I wrote ≥ here in this first expression, not just >) Similarly, y ≥ 0 However, we are given here that xy doesn't equal 0. This means x ≠ 0 and y ≠ 0.This is the reason why we can write x > 0 and y > 0 Adding the two inequalities, we get: x + y > 0 This means x  y > 0 (since x + y = xy) Or, (x+y) > 0 That is, x+ y < 0 Here is a variation of the above question that highlights the importance of the green statement above: If x  + y  = x – y, which of the following can be true?
I. x + y < 0 II. x + y = 0 III. xy = 0
(A) I only (B) III only (C) I and II only (D) II and III only (E) I, II and IIIHope this helped! Best Regards Japinder
_________________
Register for free sessions Number Properties  Algebra Quant Workshop
Success Stories Guillermo's Success Story  Carrie's Success Story
Ace GMAT quant Articles and Question to reach Q51  Question of the week
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2 Word Problems – Percentage 1  Percentage 2  Time and Work 1  Time and Work 2  Time, Speed and Distance 1  Time, Speed and Distance 2 Advanced Topics Permutation and Combination 1  Permutation and Combination 2  Permutation and Combination 3  Probability Geometry Triangles 1  Triangles 2  Triangles 3  Common Mistakes in Geometry Algebra Wavy line  Inequalities Practice Questions Number Properties 1  Number Properties 2  Algebra 1  Geometry  Prime Numbers  Absolute value equations  Sets
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4224
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: If x  + y  = x – y and xy does not equal 0, which of the followin
[#permalink]
Show Tags
07 May 2016, 09:27
bimalr9 wrote: IF x + y  =x – y and XY does not equal to 0, which of the following must be true? A. x + y > 0 B. X+Y < 0 C. XY> 0 D. XY < 0. E. X^2  Y^2 > 0 This is how I solved. What is the correct way to do this problem? I assumed the only possible value of x and y to be negative as positive value will not satisfy the given information. Taking X as 1 and Y as 1. Now, 1+1 =  (1) + (1) == > 2 = 2. Based on this I chose ‘B’ as answer. (–X) + (Y) <0. IMHO that's the perfect , shortest and the best approach to deal with the Particular problem, though there are numerous approaches for solving this problem as discussed above.. Answer will hence (B) be ( Same approach)
_________________
Thanks and Regards
Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
How to use Search Function in GMAT Club  Rules for Posting in QA forum  Writing Mathematical Formulas Rules for Posting in VA forum  Request Expert's Reply ( VA Forum Only )



Director
Joined: 04 Jun 2016
Posts: 569

If x  + y  = x – y and xy does not equal 0, which of the followin
[#permalink]
Show Tags
25 Jul 2016, 01:14
Bunuel wrote: Tough and Tricky questions: Absolute Values. If x  + y  = x – y and xy does not equal 0, which of the following must be true? A. x + y > 0 B. x + y < 0 C. x – y > 0 D. x – y < 0 E. x^2 – y^2 > 0 x  + y  = x – y Lets solve LHS Anything that comes out of mod is positive so x+y = postive so x+y >0 Lets solve RHS xy (x+y) LHS =RHS (x+y)>0 1(x+y)>0 Now since we know that our expression is positive we can remove the 1 by multiplying both side of the inequality with 1 and flipping the inequality sign (Don't forget whenever we multiply an equality with a negative number we have to flip the sign !!) 1*1(x+y)<0 * (1) 1(x+y)<0 x+y<0 This is a correct match with our option B B is the answer.
_________________
Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly. FINAL GOODBYE : 17th SEPTEMBER 2016. .. 16 March 2017  I am back but for all purposes please consider me semiretired.



Intern
Joined: 21 Sep 2016
Posts: 2
Location: United States (VA)
GPA: 3.2

Re: If x + y = x y and xy does not equal 0, which of the following
[#permalink]
Show Tags
21 Sep 2016, 10:55
achintsodhi wrote: if x + y = x y and xy does not equal 0, which of the following must be true ?
a)\(x+y>0\) b)\(x +y<0\) c) \(xy >0\) d) \(xy<0\) e) \(x^2Y^2>0\)
Please give explanations for your answers as well. My second post ever... x + y is always > 0; Therefore x  y > 0 1*(x + y) > 0 x + y < 0



Intern
Joined: 02 Apr 2016
Posts: 10

Re: If x + y = x y and xy does not equal 0, which of the following
[#permalink]
Show Tags
21 Sep 2016, 11:22
x +y is always positive Thus, x y is positive . So we can say that x and y are negative . So sum of two negative number is negative Sent from my Nexus 4 using GMAT Club Forum mobile app



Intern
Joined: 16 Mar 2017
Posts: 11
GPA: 3.87

Re: If x  + y  = x – y and xy does not equal 0, which of the followin
[#permalink]
Show Tags
15 May 2017, 23:04
Bunuel wrote: Tough and Tricky questions: Absolute Values. If x  + y  = x – y and xy does not equal 0, which of the following must be true? A. x + y > 0 B. x + y < 0 C. x – y > 0 D. x – y < 0 E. x^2 – y^2 > 0 We know that absolute values are always positive. Therefore, x  + y  > 0. As x  + y  = x – y, then x – y > 0 x – y= (x+y) and (x+y) > 0 To remove the negative sign, one must swap the inequality, So (x+y) < 0 B
_________________
Lina



Manager
Joined: 27 Aug 2016
Posts: 89
Location: India
GPA: 3
WE: Engineering (Energy and Utilities)

Re: If x  + y  = x – y and xy does not equal 0, which of the followin
[#permalink]
Show Tags
16 May 2017, 08:05
Bunuel wrote: Tough and Tricky questions: Absolute Values. If x  + y  = x – y and xy does not equal 0, which of the following must be true? A. x + y > 0 B. x + y < 0 C. x – y > 0 D. x – y < 0 E. x^2 – y^2 > 0 I thought about the question as under: LHS> distance of x from zero + distance of y from zero i.e. something positive RHS> it MUST be positive, a quick glance over the options reveals B as the amswer.... took about 20 seconds Pl correct me if i have been plain lucky kudos if i it helps



SVP
Joined: 26 Mar 2013
Posts: 1882

If x  + y  = x – y and xy does not equal 0, which of the followin
[#permalink]
Show Tags
08 Oct 2017, 23:50
Bunuel wrote: Tough and Tricky questions: Absolute Values. If x  + y  = x – y and xy does not equal 0, which of the following must be true? A. x + y > 0 B. x + y < 0 C. x – y > 0 D. x – y < 0 E. x^2 – y^2 > 0 When dealing with this question, it maybe solved with logic or plugin numbers or both. \(xy\neq{0}\)......\(x\neq{0}\) & \(y\neq{0}\) Analyzing RHS: \(x  + y \) = any number with any sign  + any number with any sign = POSITIVE NumberAnalyzing LHS: \(x – y =  (x+y)\) .......MUST BE positive to match RHS \( (x+y) > 0\)....then \(x+y<0\) Answer: B Another approachPlugin numbers. Here sense of numbers says 2 notes: 1 It useless to use positive examples 2 No restriction if x=y. This note will help to DISPROVE the choices as all related to zero 3 In absolute questions, I usually prefer to start with negative values Let \(x = y = 2\) \(x y = 0\) x  y = 0.........It means choices C, D & E are disproved........ Eliminate x + y = 4 Choice A is disapproved.................. Eliminate Answer: B



Manager
Joined: 21 Jun 2017
Posts: 84

Re: If x  + y  = x – y and xy does not equal 0, which of the followin
[#permalink]
Show Tags
13 Oct 2017, 08:00
Bunuel wrote: Tough and Tricky questions: Absolute Values. If x  + y  = x – y and xy does not equal 0, which of the following must be true? A. x + y > 0 B. x + y < 0 C. x – y > 0 D. x – y < 0 E. x^2 – y^2 > 0 x + y > 0 xy>0; therefore, at least one is negative factor our the negative = (x+y)>0 therefore x+y <0 Answer B




Re: If x  + y  = x – y and xy does not equal 0, which of the followin &nbs
[#permalink]
13 Oct 2017, 08:00



Go to page
1 2
Next
[ 21 posts ]



