January 19, 2019 January 19, 2019 07:00 AM PST 09:00 AM PST Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. January 20, 2019 January 20, 2019 07:00 AM PST 07:00 AM PST Get personalized insights on how to achieve your Target Quant Score.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 16 May 2009
Posts: 28

If x  y = x+y and xy not equal zero , which of the following
[#permalink]
Show Tags
09 Sep 2009, 09:11
Question Stats:
64% (01:19) correct 36% (01:23) wrong based on 896 sessions
HideShow timer Statistics
If x  y = x+y and xy not equal zero , which of the following must be true ? A. xy> 0 B. xy< 0 C. x+y> 0 D. xy>0 E. xy<0
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 52285

Re: PS  Number system
[#permalink]
Show Tags
14 Jul 2010, 04:56
divakarbio7 wrote: if lxl  lyl = lx+yl anf xy does , not equal to o, which of the following must be true?
A. xy > 0 B. xy < 0 C. x+y >0 D. xy>0 E. xy<0 \(xy=x+y\) > square both sides > \((xy)^2=(x+y)^2\) > note that \((x+y)^2=(x+y)^2\) > \((xy)^2=(x+y)^2\) > \(x^22xy+y^2=x^2+2xy+y^2\) > \(xy=xy\) > \(xy\leq{0}\), but as given that \(xy\neq{0}\), then \(xy<0\). Answer: E. Another way:Right hand side, \(x+y\), is an absolute value, which is always nonnegative, but as \(xy\neq{0}\), then in this case it's positive > \(RHS=x+y>0\). So LHS must also be more than zero \(xy>0\), or \(x>y\). So we can have following 4 scenarios: 1. 0yx: \(0<y<x\) > \(xy=xy\) and \(x+y=x+y\) > \(xy\neq{x+y}\). Not correct. 2. y0x: \(y<0<x\) > \(xy=x+y\) and \(x+y=x+y\) > \(x+y={x+y}\). Correct. 3. x0y: \(x<0<y\) > \(xy=xy\) and \(x+y=xy\) > \(xy={xy}\). Correct. 4. xy0: \(x<y<0\) > \(xy=x+y\) and \(x+y=xy\) > \(x+y\neq{xy}\). Not correct. So we have that either \(y<0<x\) (case 2) or \(x<0<y\) (case 3) > \(x\) and \(y\) have opposite signs > \(xy<0\). Answer: E. 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




Senior Manager
Joined: 13 May 2013
Posts: 425

Re: If x  y = x+y and xy does not equal to 0, which of
[#permalink]
Show Tags
30 May 2013, 15:40
I get the mechanics of flipping the signs when y is negative, but I guess I don't understand the logic.
If I take an absolute value of a number (always positive) then subtract from it an absolute value of a smaller number, which is negative how does that end up being X+Y? Are we looking just for the values of x and y, as opposed to the values of xy?




Intern
Joined: 03 Sep 2009
Posts: 29

Re: If x  y = x+y and xy not equal zero , which of the following
[#permalink]
Show Tags
09 Sep 2009, 09:44
x  y = x+y => (x  y)^2 = x+y^2 = (x+y)^2 => x^2  2xy + y^2 = x^2 + 2xy + y^2 => xy = xy because xy != 0 so xy <0 Ans: E Pedros wrote: if x  y = x+y and xy not equal zero , which of the following must be true ? a) xy> 0 b) xy< 0 c) x+y> 0 d) xy>0 e) xy<0 this one is from manhattan, the answer is I want to know wether there is a rule involved that i am missing, or an effective strategy to tackle that kind of questions Thank you



Math Expert
Joined: 02 Aug 2009
Posts: 7201

Re: If x  y = x+y and xy not equal zero , which of the following
[#permalink]
Show Tags
09 Sep 2009, 10:35
there can be 4 instances: i)x +,y ....x  y = x+y => xy=xy ii) both +... xy=x+y.. not possible as xy not equal zero iii) both ....xy=(x+y) .. not possible as xy not equal zero iv) x,y+...xy=yx......x=y.. therefore x and y are of different signs, when multiplied ,it should be ive
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Intern
Joined: 29 Nov 2009
Posts: 25
Location: Bangalore  INDIA
Schools: Duke, NUS,Rutgers
WE 1: Health & Life Science

If x  y = x+y and xy does not equal to 0, which of
[#permalink]
Show Tags
Updated on: 04 Dec 2012, 01:11
If x  y = x+y and xy does not equal to 0, which of the following must be true?
A. xy > 0 B. xy < 0 C. x+y > 0 D. xy > 0 E. xy < 0
Originally posted by divakarbio7 on 13 Jul 2010, 22:00.
Last edited by Bunuel on 04 Dec 2012, 01:11, edited 1 time in total.
Renamed the topic and edited the question.



Intern
Joined: 09 Oct 2009
Posts: 42

Re: PS  Number system
[#permalink]
Show Tags
15 Jul 2010, 04:12
divakarbio7 wrote: if lxl  lyl = lx+yl anf xy does , not equal to o, which of the following must be true?
A. xy > 0 B. xy < 0 C. x+y >0 D. xy>0 E. xy<0 Also, if you're short on time, and since you know that xy is not 0, then you know it MUST be greater than or less than 0, so you can narrow your choices down to D or E.



Manager
Joined: 06 Apr 2010
Posts: 69

Re: PS  Number system
[#permalink]
Show Tags
01 Sep 2010, 04:03
SnehaC wrote: divakarbio7 wrote: if lxl  lyl = lx+yl anf xy does , not equal to o, which of the following must be true?
A. xy > 0 B. xy < 0 C. x+y >0 D. xy>0 E. xy<0 Also, if you're short on time, and since you know that xy is not 0, then you know it MUST be greater than or less than 0, so you can narrow your choices down to D or E. the only way lxl  lyl can equal lx+yl is when one number is positive and one number is negative or both are zero. So then xy must be negative. I think I read if somewhere in Bunuel's post



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8792
Location: Pune, India

Re: If x  y = x+y and xy not equal zero , which of the following
[#permalink]
Show Tags
14 Jun 2011, 20:05
Pedros wrote: if x  y = x+y and xy not equal zero , which of the following must be true ? a) xy> 0 b) xy< 0 c) x+y> 0 d) xy>0 e) xy<0 this one is from manhattan, the answer is I want to know wether there is a rule involved that i am missing, or an effective strategy to tackle that kind of questions Thank you mnpqxyzt has given a great solution above. I would like to add here that it is possible that it doesn't occur to you that you should square both sides. If you do get stuck with such a question, notice that it says 'which of the following MUST be true'. So as a back up, you can rely on plugging in numbers. If you get even one set of values for which the condition does not hold, the condition is not your answer. x  y = x+y First set of nonzero values that come to mind is x = 1, y = 1 This set satisfies only options (A) and (E). Now, the set x = 1, y = 1 will also satisfy the given equation. But this set will not satisfy option (A). Hence answer (E).
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Manager
Joined: 11 Feb 2011
Posts: 112

Re: If x  y = x+y and xy not equal zero , which of the following
[#permalink]
Show Tags
18 Jun 2011, 20:49
Krishma can you pls explain how to eliminate answer choices precisely.How can xy<0 not be true when one is negative and the other positive.
_________________
target:810 out of 800!



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8792
Location: Pune, India

Re: If x  y = x+y and xy not equal zero , which of the following
[#permalink]
Show Tags
19 Jun 2011, 03:57
AnkitK wrote: Krishma can you pls explain how to eliminate answer choices precisely.How can xy<0 not be true when one is negative and the other positive. Ok. Given: x  y = x+y There are infinite set of values for x and y that satisfy this equation. Let us try one of them. Say x = 1, y = 1 a) xy> 0 .......... 1  (1) > 0; 2 > 0; True b) xy< 0........... 1  (1) < 0; 2 < 0; Eliminate c) x+y> 0........... 1 + (1) > 0; 0 > 0; Eliminate d) xy>0.............. 1 *(1) > 0; 1 > 0; Eliminate e) xy<0.............. 1 *(1) < 0; 1 < 0; True So I have two options that satisfy the assumed values of x and y. We need to eliminate one of them. They are a) xy> 0 e) xy<0 We see that x = 1, y = 1 satisfies both these inequalities. But option (a) is not symmetric i.e. if you interchange the values of x and y, it will not hold. That is, if x = 1 and y = 1, our original equation x  y = x+y is still satisfied but a) xy> 0 .............. (1)  (1) > 0; 2>0; False. Eliminate e) xy<0................. (1)(1) < 0; True Since option (e) still holds, it is the answer. xy<0 is certainly true when one of them is negative and the other is positive. Takeaways: x + y = x+y when x and y have the same signs  either both are positive or both are negative (or one or both of them are 0) x  y = x+y when x and y have opposite signs  one is positive, the other negative (or y is 0 or both are 0)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Manager
Status: On...
Joined: 16 Jan 2011
Posts: 163

Re: If x  y = x+y and xy not equal zero , which of the following
[#permalink]
Show Tags
21 Jun 2011, 09:25
VeritasPrepKarishma wrote: AnkitK wrote: Krishma can you pls explain how to eliminate answer choices precisely.How can xy<0 not be true when one is negative and the other positive. Ok. Given: x  y = x+y There are infinite set of values for x and y that satisfy this equation. Let us try one of them. Say x = 1, y = 1 a) xy> 0 .......... 1  (1) > 0; 2 > 0; True b) xy< 0........... 1  (1) < 0; 2 < 0; Eliminate c) x+y> 0........... 1 + (1) > 0; 0 > 0; Eliminate d) xy>0.............. 1 *(1) > 0; 1 > 0; Eliminate e) xy<0.............. 1 *(1) < 0; 1 < 0; True So I have two options that satisfy the assumed values of x and y. We need to eliminate one of them. They are a) xy> 0 e) xy<0 We see that x = 1, y = 1 satisfies both these inequalities. But option (a) is not symmetric i.e. if you interchange the values of x and y, it will not hold. That is, if x = 1 and y = 1, our original equation x  y = x+y is still satisfied but a) xy> 0 .............. (1)  (1) > 0; 2>0; False. Eliminate e) xy<0................. (1)(1) < 0; True Since option (e) still holds, it is the answer. xy<0 is certainly true when one of them is negative and the other is positive. Takeaways: x + y = x+y when x and y have the same signs  either both are positive or both are negative (or one or both of them are 0) x  y = x+y when x and y have opposite signs  one is positive, the other negative (or y is 0 or both are 0)Karishma, I think the 2nd takeaway has some extra condition missed out : xy=x+y if and only if 1) Both have opposite signs and 2) x >= y because x, y, xy , x+y 5 ,6, 1,15 ,5 , 0 , 0 5, 4, 1 , 1 so, 5 cannot be greater than 6 for the condition to occur
_________________
Labor cost for typing this post >= Labor cost for pushing the Kudos Button http://gmatclub.com/forum/kudoswhataretheyandwhywehavethem94812.html



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8792
Location: Pune, India

Re: If x  y = x+y and xy not equal zero , which of the following
[#permalink]
Show Tags
21 Jun 2011, 10:42
krishp84 wrote: Karishma, I think the 2nd takeaway has some extra condition missed out :
xy=x+y if and only if 1) Both have opposite signs and 2) x >= y
because x, y, xy , x+y 5 ,6, 1,1 5 ,5 , 0 , 0 5, 4, 1 , 1
so, 5 cannot be greater than 6 for the condition to occur
The takeaway is that if x and y satisfy the condition xy=x+y, then they must have opposite signs (or y is 0 or both are 0). But, x and y having opposite signs is not sufficient to satisfy the condition xy=x+y. As you said, in that case we will also need to check for their absolute values. (Good thinking, btw)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Manager
Joined: 17 May 2010
Posts: 240

Re: If x  y = x+y and xy not equal zero , which of the following
[#permalink]
Show Tags
08 Jul 2011, 20:23
I plugged in numbers: X = 6, Y =3 and X = 6, Y = 3. The answer is E.
_________________
If you like my post, consider giving me KUDOS!



Senior Manager
Joined: 13 Aug 2012
Posts: 426
Concentration: Marketing, Finance
GPA: 3.23

If x  y = x+y and xy does not equal to 0, which of the fo
[#permalink]
Show Tags
03 Dec 2012, 19:27
When you see x or absolute values being tested in the GMAT, this means testing (1) positive and negative signs (2) zeroes (3) nature of x and y against each other Looking at the equation we know x  y = x + y where xy is not 0. (1) We figure that x and y are nonzeroes (2) We figure that x  y > 0. This means x > y Now, we figure the signs of the two variables by lining up possibilities (1) both negative ==> x=5,y=4 ==> 5  4 = 9 FALSE (2) both positive ==> x=5,y=4 ==> 5  4 = 5 + 4 FALSE (3) x is positive, y is negative ==> 5  4 = 54 TRUE (4) y is positive, x is negative ==> 5  4 = 5+4 TRUE Now, let's find the answer A) xy > 0 ==> 5(4) = 1 FALSE E) xy <0 ==> This is exactly what we need. x and y have both different signs. Answer: E
_________________
Impossible is nothing to God.



Intern
Joined: 22 Sep 2012
Posts: 9

Re: I need a strategy for this one.
[#permalink]
Show Tags
03 Dec 2012, 23:46
I think the best strategy is to square up the equation.
x  y = x+y
> (x  y)^2 = (x+y)^2
> x^2 + y^2  2x.y = x^2 + y^2 + 2xy
> x.y =  xy
'Cause xy#0 and x.y>=0 > xy<0



Intern
Status: Need some help
Joined: 27 Nov 2012
Posts: 8
Location: United States
Concentration: General Management, Human Resources
Schools: HBS '16, Wharton Exec '17, Kellogg 1YR '15, Sloan '16, Tuck '16, Yale '16, Duke Fuqua, Anderson FEMBA '17, Marshall '16, Cambridge, Booth, CBS, Cornell Tech '15, Berkeley Haas
GPA: 3.56
WE: Sales (Internet and New Media)

Re: If x  y = x+y and xy does not equal to 0, which of
[#permalink]
Show Tags
06 Jan 2013, 18:22
this is specific to Eden,
For your rule. what if X = 1 and Y = 2 then it would be l  1 l  l 2 l = l 1 + 2 l ... 1  2 = 1 incorrect. is this correct?



Manager
Joined: 08 Dec 2012
Posts: 61
Location: United Kingdom
WE: Engineering (Consulting)

Re: PS  Number system
[#permalink]
Show Tags
10 Feb 2013, 09:31
Bunuel wrote: divakarbio7 wrote: if lxl  lyl = lx+yl anf xy does , not equal to o, which of the following must be true?
A. xy > 0 B. xy < 0 C. x+y >0 D. xy>0 E. xy<0 \(xy=x+y\) > square both sides > \((xy)^2=(x+y)^2\) > note that \((x+y)^2=(x+y)^2\) > \((xy)^2=(x+y)^2\) > \(x^22xy+y^2=x^2+2xy+y^2\) > \(xy=xy\) > \(xy\leq{0}\), but as given that \(xy\neq{0}\), then \(xy<0\). Answer: E. Another way:Right hand side, \(x+y\), is an absolute value, which is always nonnegative, but as \(xy\neq{0}\), then in this case it's positive > \(RHS=x+y>0\). So LHS must also be more than zero \(xy>0\), or \(x>y\). So we can have following 4 scenarios: 1. 0yx: \(0<y<x\) > \(xy=xy\) and \(x+y=x+y\) > \(xy\neq{x+y}\). Not correct. 2. y0x: \(y<0<x\) > \(xy=x+y\) and \(x+y=x+y\) > \(x+y={x+y}\). Correct. 3. x0y: \(x<0<y\) > \(xy=xy\) and \(x+y=xy\) > \(xy={xy}\). Correct. 4. xy0: \(x<y<0\) > \(xy=x+y\) and \(x+y=xy\) > \(x+y\neq{xy}\). Not correct. So we have that either \(y<0<x\) (case 2) or \(x<0<y\) (case 3) > \(x\) and \(y\) have opposite signs > \(xy<0\). Answer: E. Hope it helps. Hi Bunuel, I thought an absolute value of a product can never be a negative. Could you please explain in your equation how did you progress after getting this negative?



Manager
Joined: 24 Jan 2013
Posts: 72

Re: If x  y = x+y and xy does not equal to 0, which of
[#permalink]
Show Tags
10 Feb 2013, 17:03
Basically, remember in these exercises to do square root in both sides to simplify: (x+y)^2 = (x+y)^2 or (x)^2 = x^2 And also remember that: xy=xy
Therefore, with: xy = xy I would say: xy is always equal to something negative. Solution: E.



Intern
Joined: 17 Oct 2012
Posts: 15

Re: If x  y = x+y and xy does not equal to 0, which of
[#permalink]
Show Tags
12 Mar 2013, 04:44
Let us separate LHS and RHS : 1] x  y =0 It follows the curve x=y in 1st and 2nd quadrant
2] x+y=0. It follows he curve x=y in 4rth and 2nd quadrant The common set is 2nd quadrant which implies E with the exception of origin as xy<>0
Am I wrong in my interpretation ? But this is the way I visualize the problem.




Re: If x  y = x+y and xy does not equal to 0, which of &nbs
[#permalink]
12 Mar 2013, 04:44



Go to page
1 2 3
Next
[ 50 posts ]



