Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 05 Nov 2013
Posts: 23

If (xy)^2=x^2y^2, what is the value of nonzero integer xy?
[#permalink]
Show Tags
31 Jul 2014, 07:03
Question Stats:
60% (01:06) correct 40% (01:04) wrong based on 480 sessions
HideShow timer Statistics
If (x − y)^2 = x^2 − y^2, what is the value of nonzero integer xy? (1) x = 5 (2) x − y = 0 Attachment: File comment: Screenshot of the question.
Screen Shot 20140731 at 7.45.37 PM.png [ 15.21 KiB  Viewed 11093 times ]
Official Answer and Stats are available only to registered users. Register/ Login.



Intern
Joined: 05 Nov 2013
Posts: 23

Re: If (xy)^2=x^2y^2, what is the value of nonzero integer xy?
[#permalink]
Show Tags
31 Jul 2014, 07:07
OA:
A. The left side of the equation expands to x^2−2xy+y^2=x^2−y^2. From here, you can subtract x^2 from both sides, simplifying to:
y^2−2xy=−y^2 This allows you to move all terms to the left:
2y^2−2xy=0 And then you can divide both sides by 2:
y^2−xy=0 And then because the stimulus guarantees that y is not zero, you can divide both sides by y to see that:
y−x=0 QUERY: But, y can also equal zero (y=0). If we take the value y=0 then xy=0  and not 25
Because statement 1 gives you the value of x, it is sufficient as x = y, so xy = (5)(5) = 25. Note that statement 2 is just a restatement of what you can prove from the stimulus, so it adds no new value and is not sufficient. The correct answer is A.



Math Expert
Joined: 02 Sep 2009
Posts: 50060

Re: If (xy)^2=x^2y^2, what is the value of nonzero integer xy?
[#permalink]
Show Tags
31 Jul 2014, 07:10
pratikshr wrote: If (x − y)^2 = x^2 − y^2, what is the value of nonzero integer xy?
(1) x = 5 (2) x − y = 0
OA:
A. The left side of the equation expands to x^2−2xy+y^2=x^2−y^2. From here, you can subtract x^2 from both sides, simplifying to:
y^2−2xy=−y^2 This allows you to move all terms to the left:
2y^2−2xy=0 And then you can divide both sides by 2:
y^2−xy=0 And then because the stimulus guarantees that y is not zero, you can divide both sides by y to see that:
y−x=0 QUERY: But, y can also equal zero (y=0). If we take the value y=0 then xy=0  and not 25
Because statement 1 gives you the value of x, it is sufficient as x = y, so xy = (5)(5) = 25. Note that statement 2 is just a restatement of what you can prove from the stimulus, so it adds no new value and is not sufficient. The correct answer is A. The stem explicitly states that xy is nonzero integer, which means that neither x nor y could be 0.
_________________
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



Intern
Joined: 05 Nov 2013
Posts: 23

Re: If (xy)^2=x^2y^2, what is the value of nonzero integer xy?
[#permalink]
Show Tags
31 Jul 2014, 07:13
Thanks Bunuel. That was super quick.
Kudos.



Manager
Joined: 01 Jun 2013
Posts: 110

If (xy)^2=x^2y^2, what is the value of nonzero integer xy?
[#permalink]
Show Tags
28 Sep 2015, 11:43
If (x − y)^2 = x^2 − y^2, what is the value of nonzero integer xy? (1) x = 5 (2) x − y = 0 x^2+y^22xy=x^2y^2 2y^2=2xy y=x (Now we understand from the given equation, non zero solution of the equation x=y, so as long as we know either one of those it will be sufficient to solve the problem) Statement 1 is sufficient, since it gives the value of x, and from that we can calculate xy as 5*5=25 Statement 2 is not sufficient, since it does not give us any value for x or y. Answer is A.
_________________
Please kindly click on "+1 Kudos", if you think my post is useful



Intern
Joined: 23 Jul 2013
Posts: 15

Re: If (xy)^2=x^2y^2, what is the value of nonzero integer xy?
[#permalink]
Show Tags
12 Oct 2015, 15:16
Hi, i tried solving it as shown below. Can someone guide what mistake i made here? (Xy)(xy) = (xy)(x+y) S, (xy)=(x+y) 0 = 2y Y=0 St 1 X=5. So, x(tens digit)y(units digit)= 50



Current Student
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

If (xy)^2=x^2y^2, what is the value of nonzero integer xy?
[#permalink]
Show Tags
12 Oct 2015, 15:26
Meetup wrote: Hi, i tried solving it as shown below. Can someone guide what mistake i made here? (Xy)(xy) = (xy)(x+y) S, (xy)=(x+y) 0 = 2y Y=0 St 1 X=5. So, x(tens digit)y(units digit)= 50 Be very careful with cancelling variables in equations or inequalities.After you get, (xy)(xy) = (xy)(x+y) > (xy) [xyxy]=0 > (xy)(2y)=0 > either y=0 or xy=0 but as xy is a NON ZERO integer, y can not be =0. Thus x=y. So for knowing the value of xy, either knowing the value of x or y will be sufficient. Per statement 1, x=5, exactly what you need. Sufficient. Per statement 2, x=y , this is the same as the given information and will thus make it NOT sufficient. A is the correct answer. You can not cancel (xy) from both sides as cancelling this expression means that you are assuming that x \(\neq\) y Additionally, xy doesnt mean that x is the 10s digit and y is the unit digit. xy will give you a non zero integer value. Hope this helps.



Intern
Joined: 23 Jul 2013
Posts: 15

Re: If (xy)^2=x^2y^2, what is the value of nonzero integer xy?
[#permalink]
Show Tags
12 Oct 2015, 17:45
Thanks a lot for the quick revert,
didnt get how did u get this (xy)(xy) = (xy)(x+y) > (xy) [xyxy]=0 Moreover, for the below equation, (xy) [xyxy]=0 > (xy)(2y)=0 I see it as below, (xy) [xyxy]=0  (xy) [ 2y] = 0 and not +2y as mentioned in your post... Can you see it pls? Thanks.



Current Student
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: If (xy)^2=x^2y^2, what is the value of nonzero integer xy?
[#permalink]
Show Tags
12 Oct 2015, 18:02
Meetup wrote: Thanks a lot for the quick revert,
didnt get how did u get this (xy)(xy) = (xy)(x+y) > (xy) [xyxy]=0 Moreover, for the below equation, (xy) [xyxy]=0 > (xy)(2y)=0 I see it as below, (xy) [xyxy]=0  (xy) [ 2y] = 0 and not +2y as mentioned in your post... Can you see it pls? Thanks. Sure look below. You are given, \((xy)^2=x^2y^2\)> \((xy)(xy)=(x+y)(xy)\) ...(applying the formulae, \(a^2=a*a\) and \(a^2b^2 = (a+b)(ab)\)) >\((xy)(xy)(x+y)(xy) = 0\) > \((xy)*[(xy)(x+y)] = 0\) > \((xy)*[xyxy] = 0\) etc \((xy) [xyxy]=0\)>\((xy) (2y)=0\)> multiply both sides by (1/2) > \((xy)(y)=0\) > either \(y=0\) or \(xy=0\) (> \(x=y\)) Hope this helps.



Manager
Joined: 07 May 2015
Posts: 87

Re: If (xy)^2=x^2y^2, what is the value of nonzero integer xy?
[#permalink]
Show Tags
18 Oct 2015, 13:37
Engr2012 wrote: Meetup wrote: Thanks a lot for the quick revert,
didnt get how did u get this (xy)(xy) = (xy)(x+y) > (xy) [xyxy]=0 Moreover, for the below equation, (xy) [xyxy]=0 > (xy)(2y)=0 I see it as below, (xy) [xyxy]=0  (xy) [ 2y] = 0 and not +2y as mentioned in your post... Can you see it pls? Thanks. Sure look below. You are given, \((xy)^2=x^2y^2\)> \((xy)(xy)=(x+y)(xy)\) ...(applying the formulae, \(a^2=a*a\) and \(a^2b^2 = (a+b)(ab)\)) >\((xy)(xy)(x+y)(xy) = 0\) > \((xy)*[(xy)(x+y)] = 0\) > \((xy)*[xyxy] = 0\) etc \((xy) [xyxy]=0\)>\((xy) (2y)=0\)> multiply both sides by (1/2) > \((xy)(y)=0\) > either \(y=0\) or \(xy=0\) (> \(x=y\)) Hope this helps. Hi, Can you please explain why we can not cancel out (xy) from both sides? This is not inequality so sign should not matter, right?



Math Expert
Joined: 02 Sep 2009
Posts: 50060

Re: If (xy)^2=x^2y^2, what is the value of nonzero integer xy?
[#permalink]
Show Tags
18 Oct 2015, 13:51
neeraj609 wrote: Engr2012 wrote: Meetup wrote: Thanks a lot for the quick revert,
didnt get how did u get this (xy)(xy) = (xy)(x+y) > (xy) [xyxy]=0 Moreover, for the below equation, (xy) [xyxy]=0 > (xy)(2y)=0 I see it as below, (xy) [xyxy]=0  (xy) [ 2y] = 0 and not +2y as mentioned in your post... Can you see it pls? Thanks. Sure look below. You are given, \((xy)^2=x^2y^2\)> \((xy)(xy)=(x+y)(xy)\) ...(applying the formulae, \(a^2=a*a\) and \(a^2b^2 = (a+b)(ab)\)) >\((xy)(xy)(x+y)(xy) = 0\) > \((xy)*[(xy)(x+y)] = 0\) > \((xy)*[xyxy] = 0\) etc \((xy) [xyxy]=0\)>\((xy) (2y)=0\)> multiply both sides by (1/2) > \((xy)(y)=0\) > either \(y=0\) or \(xy=0\) (> \(x=y\)) Hope this helps. Hi, Can you please explain why we can not cancel out (xy) from both sides? This is not inequality so sign should not matter, right? x  y could be 0 and we cannot divide by 0. Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We cannot divide by zero.
_________________
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



Current Student
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: If (xy)^2=x^2y^2, what is the value of nonzero integer xy?
[#permalink]
Show Tags
18 Oct 2015, 13:52
neeraj609 wrote: Engr2012 wrote: Meetup wrote: Thanks a lot for the quick revert,
didnt get how did u get this (xy)(xy) = (xy)(x+y) > (xy) [xyxy]=0 Moreover, for the below equation, (xy) [xyxy]=0 > (xy)(2y)=0 I see it as below, (xy) [xyxy]=0  (xy) [ 2y] = 0 and not +2y as mentioned in your post... Can you see it pls? Thanks. Sure look below. You are given, \((xy)^2=x^2y^2\)> \((xy)(xy)=(x+y)(xy)\) ...(applying the formulae, \(a^2=a*a\) and \(a^2b^2 = (a+b)(ab)\)) >\((xy)(xy)(x+y)(xy) = 0\) > \((xy)*[(xy)(x+y)] = 0\) > \((xy)*[xyxy] = 0\) etc \((xy) [xyxy]=0\)>\((xy) (2y)=0\)> multiply both sides by (1/2) > \((xy)(y)=0\) > either \(y=0\) or \(xy=0\) (> \(x=y\)) Hope this helps. Hi, Can you please explain why we can not cancel out (xy) from both sides? This is not inequality so sign should not matter, right? It does not matter whether you are working with inequalities or equations. The concept remains the same. You can not cancel variables out until you know for sure about the signs or their relative values. In this case, if you cancel xy from both sides, you are assuming the x can not be equal to y. This is a very dangerous assumption as you can clearly see from the correct solution. You were not given in the main question stem that 'x can not be equal to y'. If you do cancel out such variables , you will end up with a case that might be a "maybe true" in a DS question. A "maybe true" is not sufficient in DS but after you cancel out the variabes, you will end up assuming that the case is 'always true', leading to wrong selection of option. Read the solution above carefully. Hope this helps.



Manager
Joined: 07 May 2015
Posts: 87

Re: If (xy)^2=x^2y^2, what is the value of nonzero integer xy?
[#permalink]
Show Tags
18 Oct 2015, 14:00
Sure look below.
You are given, \((xy)^2=x^2y^2\)> \((xy)(xy)=(x+y)(xy)\) ...(applying the formulae, \(a^2=a*a\) and \(a^2b^2 = (a+b)(ab)\))
>\((xy)(xy)(x+y)(xy) = 0\) > \((xy)*[(xy)(x+y)] = 0\) > \((xy)*[xyxy] = 0\) etc
\((xy) [xyxy]=0\)>\((xy) (2y)=0\)> multiply both sides by (1/2) > \((xy)(y)=0\) > either \(y=0\) or \(xy=0\) (> \(x=y\))
Hope this helps.[/quote]
Hi, Can you please explain why we can not cancel out (xy) from both sides? This is not inequality so sign should not matter, right?[/quote]
It does not matter whether you are working with inequalities or equations. The concept remains the same. You can not cancel variables out until you know for sure about the signs or their relative values.
In this case, if you cancel xy from both sides, you are assuming the x can not be equal to y. This is a very dangerous assumption as you can clearly see from the correct solution. You were not given in the main question stem that 'x can not be equal to y'.
If you do cancel out such variables , you will end up with a case that might be a "maybe true" in a DS question. A "maybe true" is not sufficient in DS but after you cancel out the variabes, you will end up assuming that the case is 'always true', leading to wrong selection of option.
Read the solution above carefully.
Hope this helps.[/quote]
Hi, thanks alot for the response!
I am sure I am missing something very basic here. Even if x=y then, (xy) = 0 which satisfies the equation given right?



Current Student
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: If (xy)^2=x^2y^2, what is the value of nonzero integer xy?
[#permalink]
Show Tags
18 Oct 2015, 14:06
neeraj609 wrote: Hi, thanks alot for the response!
I am sure I am missing something very basic here. Even if x=y then, (xy) = 0 which satisfies the equation given right?
No. If you look carefully, the question stem mentions that xy = integer and NON ZERO value. Now if I give you the scenario x=y=0, then this goes against this given information and is hence not allowed. Additionally, as Bunuel mentioned above, if xy=0, then you will end up dividing the given expression \((xy)^2=x^2y^2\) by \((xy)\) in order to 'eliminate' \((xy)\). You can not divide by a number =0 as it becomes not defined function in maths. Hope this helps.



Manager
Joined: 07 May 2015
Posts: 87

Re: If (xy)^2=x^2y^2, what is the value of nonzero integer xy?
[#permalink]
Show Tags
18 Oct 2015, 15:05
Engr2012 wrote: neeraj609 wrote: Hi, thanks alot for the response!
I am sure I am missing something very basic here. Even if x=y then, (xy) = 0 which satisfies the equation given right?
No. If you look carefully, the question stem mentions that xy = integer and NON ZERO value. Now if I give you the scenario x=y=0, then this goes against this given information and is hence not allowed. Additionally, as Bunuel mentioned above, if xy=0, then you will end up dividing the given expression \((xy)^2=x^2y^2\) by \((xy)\) in order to 'eliminate' \((xy)\). You can not divide by a number =0 as it becomes not defined function in maths. Hope this helps. Perfect, thank you so much for explaining this!!!



Current Student
Joined: 12 Aug 2015
Posts: 287
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37 GMAT 2: 650 Q43 V36 GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)

If (x−y)2=x2−y2, what is the value of nonzero integer xy? (1) x=5 (2)
[#permalink]
Show Tags
07 Dec 2015, 04:40
If (x−y)^2=x^2−y^2, what is the value of nonzero integer xy? (1) x=5 (2) x−y=0
_________________
KUDO me plenty



Math Expert
Joined: 02 Aug 2009
Posts: 6983

Re: If (x−y)2=x2−y2, what is the value of nonzero integer xy? (1) x=5 (2)
[#permalink]
Show Tags
07 Dec 2015, 04:50
shasadou wrote: If (x−y)^2=x^2−y^2, what is the value of nonzero integer xy?
(1) x=5 (2) x−y=0 Hi, after simplification, the equation tells you that either y=0 or y=x.. but it is given that both x and y are non zero integer, so x=y.. we are asked value of xy, so we require value of x or y.. 1) x=5 suff.. 2) xy=0.. it does not give us any new info.. insuff A
_________________
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



Math Expert
Joined: 02 Sep 2009
Posts: 50060

Re: If (xy)^2=x^2y^2, what is the value of nonzero integer xy?
[#permalink]
Show Tags
07 Dec 2015, 05:30



Manager
Joined: 24 Sep 2018
Posts: 131

Re: If (xy)^2=x^2y^2, what is the value of nonzero integer xy?
[#permalink]
Show Tags
02 Oct 2018, 11:10
Statement 1. Quote: The left side of the equation expands to \(x^2−2xy+y^2=x^2−y^2\) From here, we can subtract \(x^2\) from both sides, simplifying to:
\(y^2−2xy=−y^2\)
This allows us to move all terms to the left: \(2y^2−2xy=0\)
And then we can divide both sides by 2:
\(y^2−xy=0\) And then because the stimulus guarantees that y is not zero, we can divide both sides by y to see that:
y−x=0
Because statement 1 gives us the value of x, it is sufficient as x=y,
so\(, xy=(5)(5)=25\) Statement 2 Quote: It is just a restatement of what we can prove from the stimulus, so it adds no new value and is not sufficient. The correct answer is A
_________________
Please award kudos, If this post helped you in someway.




Re: If (xy)^2=x^2y^2, what is the value of nonzero integer xy? &nbs
[#permalink]
02 Oct 2018, 11:10






