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

 It is currently 15 Oct 2019, 11:54 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If x and y are integers and -x < y < x, does (x^2 - y^2)^(1/2) = x + y

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58340
Re: If x and y are integers and -x < y < x, does (x^2 - y^2)^(1/2) = x + y  [#permalink]

Show Tags

2
GMATinsight wrote:
Bunuel wrote:
If x and y are integers and $$-x \leq y \leq x$$, does $$\sqrt{x^2 - y^2} = x + y$$?

(1) |xy| is NOT a square of an integer
(2) Point (x, y) is above x-axis

SOLUTION (OE) IS HERE.

√(x^2-y^2) = (x+y)
Only If y=0

Each statement says that y#0
Hence sufficient

There is another possibility, when x = -y. For example, x = 1 and y = -1.
_________________
CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2974
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: If x and y are integers and -x < y < x, does (x^2 - y^2)^(1/2) = x + y  [#permalink]

Show Tags

Bunuel wrote:
GMATinsight wrote:
Bunuel wrote:
If x and y are integers and $$-x \leq y \leq x$$, does $$\sqrt{x^2 - y^2} = x + y$$?

(1) |xy| is NOT a square of an integer
(2) Point (x, y) is above x-axis

SOLUTION (OE) IS HERE.

√(x^2-y^2) = (x+y)
Only If y=0

Each statement says that y#0
Hence sufficient

There is another possibility, when x = -y. For example, x = 1 and y = -1.

Good point... +1Kudos
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Director  D
Joined: 13 Mar 2017
Posts: 728
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
If x and y are integers and -x < y < x, does (x^2 - y^2)^(1/2) = x + y  [#permalink]

Show Tags

Bunuel wrote:
If x and y are integers and $$-x \leq y \leq x$$, does $$\sqrt{x^2 - y^2} = x + y$$?

(1) |xy| is NOT a square of an integer
(2) Point (x, y) is above x-axis

SOLUTION (OE) IS HERE.

$$\sqrt{x^2 - y^2} = x + y$$
-> x^2-y^2 = (x+y)^2
-> (x+y)(x-y ) = (x+y)^2
(x+y )(y) = 0
-> Either y =0 or x = -y which we require .............................................................DS

Option 1 : |xy| is NOT a square of an integer
so x =/= y,-y,0 .. Since these values will make the value |xy| as a square of an integer.

Hence SUFFICIENT.

Option 2 : Point (x, y) is above x-axis, So y>0
Also y=/= 0,

Now since -x<=y <= x....
Since y>0, y =/=-x

Hence SUFFICIENT....
_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
Intern  B
Joined: 24 Jan 2017
Posts: 10
Re: If x and y are integers and -x < y < x, does (x^2 - y^2)^(1/2) = x + y  [#permalink]

Show Tags

Squaring both sides we get 2y(x+y) = 0 , so the question becomes "Is 2y(x+y) =0 ?" or y =0 or x=-y ?

Statement 1:

|xy| != perfect square ..
means x!=y or x!=-y , but Y could be zero, or non-zero. Not Sufficient

Statement 2 :

Point (x,y) is above X- axis.

Therefore, y>0 and x = anything.

Point could be (-3,3) or ( -4,3)

So, NOT Sufficient .

Correct me if i am wrong.

2y(x+y) =0 ... can't we expand it further? we can. The final equation will be x+y=0
Math Expert V
Joined: 02 Sep 2009
Posts: 58340
Re: If x and y are integers and -x < y < x, does (x^2 - y^2)^(1/2) = x + y  [#permalink]

Show Tags

seeker14 wrote:
Squaring both sides we get 2y(x+y) = 0 , so the question becomes "Is 2y(x+y) =0 ?" or y =0 or x=-y ?

Statement 1:

|xy| != perfect square ..
means x!=y or x!=-y , but Y could be zero, or non-zero. Not Sufficient

Statement 2 :

Point (x,y) is above X- axis.

Therefore, y>0 and x = anything.

Point could be (-3,3) or ( -4,3)

So, NOT Sufficient .

Correct me if i am wrong.

2y(x+y) =0 ... can't we expand it further? we can. The final equation will be x+y=0

That's not correct. $$y(x+y)=0$$ means $$y=0$$ or $$x=-y$$.

I suggest to read solution HERE.
_________________
Non-Human User Joined: 09 Sep 2013
Posts: 13172
Re: If x and y are integers and -x < y < x, does (x^2 - y^2)^(1/2) = x + y  [#permalink]

Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: If x and y are integers and -x < y < x, does (x^2 - y^2)^(1/2) = x + y   [#permalink] 09 Mar 2019, 01:07

Go to page   Previous    1   2   [ 26 posts ]

Display posts from previous: Sort by

If x and y are integers and -x < y < x, does (x^2 - y^2)^(1/2) = x + y

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  