Last visit was: 24 Apr 2026, 10:57 It is currently 24 Apr 2026, 10:57
Home
Messages
Tests
Schools
Events
Close
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
Your Progress

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
655-705 (Hard)|   Algebra|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,814
Own Kudos:
811,042
 [3]
Given Kudos: 105,873
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,814
Kudos: 811,042
 [3]
If x is an integer, is (x^2 + y^2)^(1/2) an integer? 14 May 2017, 11:31
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

65% (hard)

Question Stats:

44% (01:40) correct 56% (01:31) wrong based on 78 sessions

History

Date
Time
Result
Not Attempted Yet
If x is an integer, is \(\sqrt{x^2 + y^2}\) an integer?

(1) \(x^2 − y^2 = 0\)

(2) \(x^2 − k^2 = −y^2\) for some positive integer k
ShowHide Answer
Official Answer
D
User avatar
gmatexam439
User avatar
Moderator
Joined: 28 Mar 2017
Last visit: 18 Oct 2024
Posts: 1,054
Own Kudos:
2,195
Given Kudos: 200
Location: India
Concentration: Finance, Technology
Schools: McDonough '21 (A$) Jones '21 (A$) Kelley '23 (A)
GMAT 1: 730 Q49 V41
GPA: 4
Products:
My Reviews
Schools: McDonough '21 (A$) Jones '21 (A$) Kelley '23 (A)
GMAT 1: 730 Q49 V41
Posts: 1,054
Kudos: 2,195
If x is an integer, is (x^2 + y^2)^(1/2) an integer? 14 May 2017, 12:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If x is an integer, is \(\sqrt{x^2 + y^2}\) an integer?

(1) \(x^2 − y^2 = 0\)

(2) \(x^2 − k^2 = −y^2\) for some positive integer k
Show more

D

1. root 2*x will never be an integer
sufficient

2.root K^2 will always be an integer
sufficient
User avatar
sauravleo123
User avatar
Joined: 27 Dec 2012
Last visit: 04 May 2020
Posts: 108
Own Kudos:
274
Given Kudos: 23
Posts: 108
Kudos: 274
If x is an integer, is (x^2 + y^2)^(1/2) an integer? 14 May 2017, 22:33
Kudos
Add Kudos
Bookmarks
Bookmark this Post
x^2-y^2=0
so x=y or x=-y
so we get root 2 * y
We dont know y
if y = root 2
then above expression = int
if not then no
Insufficient
Statement 2 is obviously sufficient
B
User avatar
amanvermagmat
User avatar
Retired Moderator
Joined: 22 Aug 2013
Last visit: 28 Mar 2025
Posts: 1,142
Own Kudos:
2,973
Given Kudos: 480
Location: India
Posts: 1,142
Kudos: 2,973
If x is an integer, is (x^2 + y^2)^(1/2) an integer? 14 May 2017, 23:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The required will be an integer if and only if (x^2 + y^2) is a perfect square. If (x^2 + y^2) is NOT a perfect square, then its square root will NOT be an integer.

Statement 1. x^2 = y^2 so we can say that x^2 + y^2 = 2x^2.

But 2x^2 Could be a perfect square if x = 0 (then square root of 2x^2 will be 0, which is an integer)

and for all other integer values of x, its NOT a perfect square (try putting any other integer value of x). so Insufficient.

Statement 2. x^2 - k^2 = -y^2
or x^2 + y^2 = k^2

Now k^2 will definitely be a perfect square since k is a positive integer, so its square root will be a positive integer.
Sufficient.

Hence B
User avatar
msk0657
User avatar
Retired Moderator
Joined: 26 Nov 2012
Last visit: 14 Feb 2020
Posts: 455
Own Kudos:
569
Given Kudos: 46
Posts: 455
Kudos: 569
If x is an integer, is (x^2 + y^2)^(1/2) an integer? 14 May 2017, 23:23
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If x is an integer, is \(\sqrt{x^2 + y^2}\) an integer?

(1) \(x^2 − y^2 = 0\)

(2) \(x^2 − k^2 = −y^2\) for some positive integer k
Show more

Given \(\sqrt{x^2 + y^2}\) ...we need to find this results in integer .

Stat 1: \(x^2 − y^2 = 0\) => \(x^2 = y^2\)...Now substitute the \(y^2\) value in equation then we get \(\sqrt{x^2 + x^2}\)..

From question stem we are given that x is an integer then we'll get \(\sqrt{2}\)*x...here x is an integer but \(\sqrt{2}\) is not...since this is yes or no question ...we can say definte NO...Sufficient.

Stat 2: \(x^2 − k^2 = −y^2\) => \(x^2 + y^2 = k^2\)...sub this value then we get \(\sqrt{k^2}\)....and since k is an integer the result in integer..Sufficient.

Option D.
User avatar
Shruti0805
User avatar
Joined: 24 Dec 2016
Last visit: 02 Sep 2021
Posts: 91
Own Kudos:
49
Given Kudos: 145
Location: India
Concentration: Finance, General Management
Schools: Simon '21 (A$) Carlson '21 (A$) McDonough '21 (A)
WE:Information Technology (Computer Software)
Schools: Simon '21 (A$) Carlson '21 (A$) McDonough '21 (A)
Posts: 91
Kudos: 49
If x is an integer, is (x^2 + y^2)^(1/2) an integer? 15 May 2017, 23:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
On the GMAT, can we have instances on a Yes/No DS question where one of the statements gives a No answer but the other gives a Yes ?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,814
Own Kudos:
811,042
Given Kudos: 105,873
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,814
Kudos: 811,042
If x is an integer, is (x^2 + y^2)^(1/2) an integer? 15 May 2017, 23:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Shruti0805
On the GMAT, can we have instances on a Yes/No DS question where one of the statements gives a No answer but the other gives a Yes ?
Show more

No.

On the GMAT, two data sufficiency statements always provide TRUE information and these statements NEVER contradict each other or the stem. So, if you get a definite YES answer to the question from (1) you cannot get a definite NO answer from (2). Or say if you get that x = 2 only from (1) you cannot get x = 3 only from (2).
User avatar
amanvermagmat
User avatar
Retired Moderator
Joined: 22 Aug 2013
Last visit: 28 Mar 2025
Posts: 1,142
Own Kudos:
2,973
Given Kudos: 480
Location: India
Posts: 1,142
Kudos: 2,973
If x is an integer, is (x^2 + y^2)^(1/2) an integer? 15 May 2017, 23:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Shruti0805
On the GMAT, can we have instances on a Yes/No DS question where one of the statements gives a No answer but the other gives a Yes ?
Show more
Good question. As per GMAT history, I don't think such an instance has ever occurred. Experts here can guide us better.

And anyway, as I wrote in my explanation, answer should be B not D.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,814
Own Kudos:
811,042
Given Kudos: 105,873
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,814
Kudos: 811,042
If x is an integer, is (x^2 + y^2)^(1/2) an integer? 15 May 2017, 23:52
Kudos
Add Kudos
Bookmarks
Bookmark this Post
amanvermagmat
Shruti0805
On the GMAT, can we have instances on a Yes/No DS question where one of the statements gives a No answer but the other gives a Yes ?
Good question. As per GMAT history, I don't think such an instance has ever occurred. Experts here can guide us better.

And anyway, as I wrote in my explanation, answer should be B not D.
Show more

I answered this here: https://gmatclub.com/forum/if-x-is-an-i ... l#p1852776
User avatar
mohshu
User avatar
Joined: 21 Mar 2016
Last visit: 26 Dec 2019
Posts: 410
Own Kudos:
143
Given Kudos: 103
Products:
My Reviews
Posts: 410
Kudos: 143
If x is an integer, is (x^2 + y^2)^(1/2) an integer? 17 May 2017, 09:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
stat1 : says x^2 = y^2
substitute in the stem,, suff,,,
given x is a integer,,

stat2 : clearly suff,,

ans D
Moderators:
Bunuel
Math Expert
109814 posts
kingbucky
498 posts
Gmat860sanskar
212 posts