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If x  + y  = x – y and xy does not equal 0, which of the followin [#permalink]
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15 Oct 2014, 16:42
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Re: If x  + y  = x – y and xy does not equal 0, which of the followin [#permalink]
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15 Oct 2014, 20:12
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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



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Re: If x  + y  = x – y and xy does not equal 0, which of the followin [#permalink]
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15 Oct 2014, 20:28
From given equation, it can be easily deduced that x<0, y<0 so (ve) + (ve) = (ve) < 0



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Re: If x  + y  = x – y and xy does not equal 0, which of the followin [#permalink]
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16 Oct 2014, 22:05
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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
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Re: If x  + y  = x – y and xy does not equal 0, which of the followin [#permalink]
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17 Oct 2014, 10:54
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 !



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Re: If x  + y  = x – y and xy does not equal 0, which of the followin [#permalink]
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18 Oct 2014, 04:15
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....
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Re: If x  + y  = x – y and xy does not equal 0, which of the followin [#permalink]
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18 Oct 2014, 07:46
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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



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Re: If x  + y  = x – y and xy does not equal 0, which of the followin [#permalink]
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01 Jan 2015, 15:07
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



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Re: If x  + y  = x – y and xy does not equal 0, which of the followin [#permalink]
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02 Jan 2015, 05:26
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.
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Re: If x  + y  = x – y and xy does not equal 0, which of the followin [#permalink]
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25 May 2015, 08:22
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x + y = xy =>  (x+y)
means that x+y<0 for their negative to be positive
B



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Re: If x  + y  = x – y and xy does not equal 0, which of the followin [#permalink]
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26 May 2015, 21:59
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
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Re: If x  + y  = x – y and xy does not equal 0, which of the followin [#permalink]
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26 May 2015, 23:38
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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
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Re: If x  + y  = x – y and xy does not equal 0, which of the followin [#permalink]
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07 May 2016, 10:27
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)
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If x  + y  = x – y and xy does not equal 0, which of the followin [#permalink]
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25 Jul 2016, 02:14
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.
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Re: If x + y = x y and xy does not equal 0, which of the following [#permalink]
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21 Sep 2016, 11:55
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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



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Re: If x + y = x y and xy does not equal 0, which of the following [#permalink]
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21 Sep 2016, 12:22
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



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Re: If x  + y  = x – y and xy does not equal 0, which of the followin [#permalink]
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16 May 2017, 00:04
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
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Re: If x  + y  = x – y and xy does not equal 0, which of the followin [#permalink]
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16 May 2017, 09:05
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



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If x  + y  = x – y and xy does not equal 0, which of the followin [#permalink]
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09 Oct 2017, 00:50
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



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Re: If x  + y  = x – y and xy does not equal 0, which of the followin [#permalink]
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13 Oct 2017, 09:00
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




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