GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 12 Dec 2018, 00:31

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### The winning strategy for 700+ on the GMAT

December 13, 2018

December 13, 2018

08:00 AM PST

09:00 AM PST

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.
• ### GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

December 14, 2018

December 14, 2018

09:00 AM PST

10:00 AM PST

10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.

# If (x-y)^2=x^2-y^2, what is the value of nonzero integer xy?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 05 Nov 2013
Posts: 23
If (x-y)^2=x^2-y^2, what is the value of nonzero integer xy?  [#permalink]

### Show Tags

31 Jul 2014, 06:03
3
11
00:00

Difficulty:

55% (hard)

Question Stats:

60% (01:06) correct 40% (01:05) wrong based on 490 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 2014-07-31 at 7.45.37 PM.png [ 15.21 KiB | Viewed 11630 times ]
Intern
Joined: 05 Nov 2013
Posts: 23
Re: If (x-y)^2=x^2-y^2, what is the value of nonzero integer xy?  [#permalink]

### Show Tags

31 Jul 2014, 06:07
4
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: 51107
Re: If (x-y)^2=x^2-y^2, what is the value of nonzero integer xy?  [#permalink]

### Show Tags

31 Jul 2014, 06:10
2
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.
_________________
Intern
Joined: 05 Nov 2013
Posts: 23
Re: If (x-y)^2=x^2-y^2, what is the value of nonzero integer xy?  [#permalink]

### Show Tags

31 Jul 2014, 06:13
Thanks Bunuel. That was super quick.

Kudos.
Manager
Joined: 01 Jun 2013
Posts: 107
GMAT 1: 650 Q50 V27
If (x-y)^2=x^2-y^2, what is the value of nonzero integer xy?  [#permalink]

### Show Tags

28 Sep 2015, 10:43
1
2
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^2-2xy=x^2-y^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.

_________________

Please kindly click on "+1 Kudos", if you think my post is useful

Intern
Joined: 23 Jul 2013
Posts: 15
Re: If (x-y)^2=x^2-y^2, what is the value of nonzero integer xy?  [#permalink]

### Show Tags

12 Oct 2015, 14:16
Hi, i tried solving it as shown below. Can someone guide what mistake i made here?
(X-y)(x-y) = (x-y)(x+y)
S, (x-y)=(x+y)
0 = 2y
Y=0
St 1-
X=5. So, x(tens digit)y(units digit)= 50
CEO
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
If (x-y)^2=x^2-y^2, what is the value of nonzero integer xy?  [#permalink]

### Show Tags

12 Oct 2015, 14:26
1
Meetup wrote:
Hi, i tried solving it as shown below. Can someone guide what mistake i made here?
(X-y)(x-y) = (x-y)(x+y)
S, (x-y)=(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, (x-y)(x-y) = (x-y)(x+y) ---> (x-y) [x-y-x-y]=0 ---> (x-y)(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.

You can not cancel (x-y) 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 (x-y)^2=x^2-y^2, what is the value of nonzero integer xy?  [#permalink]

### Show Tags

12 Oct 2015, 16:45
Thanks a lot for the quick revert,

didnt get how did u get this
(x-y)(x-y) = (x-y)(x+y) ---> (x-y) [x-y-x-y]=0
Moreover, for the below equation,
(x-y) [x-y-x-y]=0 ---> (x-y)(2y)=0
I see it as below,
(x-y) [x-y-x-y]=0 --- (x-y) [ -2y] = 0 and not +2y as mentioned in your post... Can you see it pls? Thanks.
CEO
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If (x-y)^2=x^2-y^2, what is the value of nonzero integer xy?  [#permalink]

### Show Tags

12 Oct 2015, 17:02
Meetup wrote:
Thanks a lot for the quick revert,

didnt get how did u get this
(x-y)(x-y) = (x-y)(x+y) ---> (x-y) [x-y-x-y]=0
Moreover, for the below equation,
(x-y) [x-y-x-y]=0 ---> (x-y)(2y)=0
I see it as below,
(x-y) [x-y-x-y]=0 --- (x-y) [ -2y] = 0 and not +2y as mentioned in your post... Can you see it pls? Thanks.

Sure look below.

You are given, $$(x-y)^2=x^2-y^2$$---> $$(x-y)(x-y)=(x+y)(x-y)$$ ...(applying the formulae, $$a^2=a*a$$ and $$a^2-b^2 = (a+b)(a-b)$$)

--->$$(x-y)(x-y)-(x+y)(x-y) = 0$$ ---> $$(x-y)*[(x-y)-(x+y)] = 0$$ ---> $$(x-y)*[x-y-x-y] = 0$$ etc

$$(x-y) [x-y-x-y]=0$$--->$$(x-y) (-2y)=0$$---> multiply both sides by (-1/2) ---> $$(x-y)(y)=0$$ ----> either $$y=0$$ or $$x-y=0$$ (--> $$x=y$$)

Hope this helps.
Manager
Joined: 07 May 2015
Posts: 85
Re: If (x-y)^2=x^2-y^2, what is the value of nonzero integer xy?  [#permalink]

### Show Tags

18 Oct 2015, 12:37
Engr2012 wrote:
Meetup wrote:
Thanks a lot for the quick revert,

didnt get how did u get this
(x-y)(x-y) = (x-y)(x+y) ---> (x-y) [x-y-x-y]=0
Moreover, for the below equation,
(x-y) [x-y-x-y]=0 ---> (x-y)(2y)=0
I see it as below,
(x-y) [x-y-x-y]=0 --- (x-y) [ -2y] = 0 and not +2y as mentioned in your post... Can you see it pls? Thanks.

Sure look below.

You are given, $$(x-y)^2=x^2-y^2$$---> $$(x-y)(x-y)=(x+y)(x-y)$$ ...(applying the formulae, $$a^2=a*a$$ and $$a^2-b^2 = (a+b)(a-b)$$)

--->$$(x-y)(x-y)-(x+y)(x-y) = 0$$ ---> $$(x-y)*[(x-y)-(x+y)] = 0$$ ---> $$(x-y)*[x-y-x-y] = 0$$ etc

$$(x-y) [x-y-x-y]=0$$--->$$(x-y) (-2y)=0$$---> multiply both sides by (-1/2) ---> $$(x-y)(y)=0$$ ----> either $$y=0$$ or $$x-y=0$$ (--> $$x=y$$)

Hope this helps.

Hi, Can you please explain why we can not cancel out (x-y) from both sides? This is not inequality so sign should not matter, right?
Math Expert
Joined: 02 Sep 2009
Posts: 51107
Re: If (x-y)^2=x^2-y^2, what is the value of nonzero integer xy?  [#permalink]

### Show Tags

18 Oct 2015, 12:51
neeraj609 wrote:
Engr2012 wrote:
Meetup wrote:
Thanks a lot for the quick revert,

didnt get how did u get this
(x-y)(x-y) = (x-y)(x+y) ---> (x-y) [x-y-x-y]=0
Moreover, for the below equation,
(x-y) [x-y-x-y]=0 ---> (x-y)(2y)=0
I see it as below,
(x-y) [x-y-x-y]=0 --- (x-y) [ -2y] = 0 and not +2y as mentioned in your post... Can you see it pls? Thanks.

Sure look below.

You are given, $$(x-y)^2=x^2-y^2$$---> $$(x-y)(x-y)=(x+y)(x-y)$$ ...(applying the formulae, $$a^2=a*a$$ and $$a^2-b^2 = (a+b)(a-b)$$)

--->$$(x-y)(x-y)-(x+y)(x-y) = 0$$ ---> $$(x-y)*[(x-y)-(x+y)] = 0$$ ---> $$(x-y)*[x-y-x-y] = 0$$ etc

$$(x-y) [x-y-x-y]=0$$--->$$(x-y) (-2y)=0$$---> multiply both sides by (-1/2) ---> $$(x-y)(y)=0$$ ----> either $$y=0$$ or $$x-y=0$$ (--> $$x=y$$)

Hope this helps.

Hi, Can you please explain why we can not cancel out (x-y) 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.
_________________
CEO
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If (x-y)^2=x^2-y^2, what is the value of nonzero integer xy?  [#permalink]

### Show Tags

18 Oct 2015, 12:52
1
neeraj609 wrote:
Engr2012 wrote:
Meetup wrote:
Thanks a lot for the quick revert,

didnt get how did u get this
(x-y)(x-y) = (x-y)(x+y) ---> (x-y) [x-y-x-y]=0
Moreover, for the below equation,
(x-y) [x-y-x-y]=0 ---> (x-y)(2y)=0
I see it as below,
(x-y) [x-y-x-y]=0 --- (x-y) [ -2y] = 0 and not +2y as mentioned in your post... Can you see it pls? Thanks.

Sure look below.

You are given, $$(x-y)^2=x^2-y^2$$---> $$(x-y)(x-y)=(x+y)(x-y)$$ ...(applying the formulae, $$a^2=a*a$$ and $$a^2-b^2 = (a+b)(a-b)$$)

--->$$(x-y)(x-y)-(x+y)(x-y) = 0$$ ---> $$(x-y)*[(x-y)-(x+y)] = 0$$ ---> $$(x-y)*[x-y-x-y] = 0$$ etc

$$(x-y) [x-y-x-y]=0$$--->$$(x-y) (-2y)=0$$---> multiply both sides by (-1/2) ---> $$(x-y)(y)=0$$ ----> either $$y=0$$ or $$x-y=0$$ (--> $$x=y$$)

Hope this helps.

Hi, Can you please explain why we can not cancel out (x-y) 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 x-y 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.

Hope this helps.
Manager
Joined: 07 May 2015
Posts: 85
Re: If (x-y)^2=x^2-y^2, what is the value of nonzero integer xy?  [#permalink]

### Show Tags

18 Oct 2015, 13:00
Sure look below.

You are given, $$(x-y)^2=x^2-y^2$$---> $$(x-y)(x-y)=(x+y)(x-y)$$ ...(applying the formulae, $$a^2=a*a$$ and $$a^2-b^2 = (a+b)(a-b)$$)

--->$$(x-y)(x-y)-(x+y)(x-y) = 0$$ ---> $$(x-y)*[(x-y)-(x+y)] = 0$$ ---> $$(x-y)*[x-y-x-y] = 0$$ etc

$$(x-y) [x-y-x-y]=0$$--->$$(x-y) (-2y)=0$$---> multiply both sides by (-1/2) ---> $$(x-y)(y)=0$$ ----> either $$y=0$$ or $$x-y=0$$ (--> $$x=y$$)

Hope this helps.[/quote]

Hi, Can you please explain why we can not cancel out (x-y) 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 x-y 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.

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, (x-y) = 0 which satisfies the equation given right?
CEO
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If (x-y)^2=x^2-y^2, what is the value of nonzero integer xy?  [#permalink]

### Show Tags

18 Oct 2015, 13:06
1
neeraj609 wrote:

Hi, thanks alot for the response!

I am sure I am missing something very basic here. Even if x=y then, (x-y) = 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 x-y=0, then you will end up dividing the given expression $$(x-y)^2=x^2-y^2$$ by $$(x-y)$$ in order to 'eliminate' $$(x-y)$$. 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: 85
Re: If (x-y)^2=x^2-y^2, what is the value of nonzero integer xy?  [#permalink]

### Show Tags

18 Oct 2015, 14:05
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, (x-y) = 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 x-y=0, then you will end up dividing the given expression $$(x-y)^2=x^2-y^2$$ by $$(x-y)$$ in order to 'eliminate' $$(x-y)$$. 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: 286
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, 03:40
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: 7102
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, 03:50
2
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) x-y=0.. it does not give us any new info.. insuff

A
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Math Expert
Joined: 02 Sep 2009
Posts: 51107
Re: If (x-y)^2=x^2-y^2, what is the value of nonzero integer xy?  [#permalink]

### Show Tags

07 Dec 2015, 04:30
If (x−y)^2=x^2−y^2, what is the value of nonzero integer xy?

(1) x=5
(2) x−y=0

Merging similar topics. Please refer to the discussion above.
_________________
Manager
Joined: 24 Sep 2018
Posts: 138
Re: If (x-y)^2=x^2-y^2, what is the value of nonzero integer xy?  [#permalink]

### Show Tags

02 Oct 2018, 10:10
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 (x-y)^2=x^2-y^2, what is the value of nonzero integer xy? &nbs [#permalink] 02 Oct 2018, 10:10
Display posts from previous: Sort by