Last visit was: 19 Jul 2024, 23:49 It is currently 19 Jul 2024, 23:49
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.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94421
Own Kudos [?]: 642418 [3]
Given Kudos: 86332
Send PM
Moderator
Joined: 28 Mar 2017
Posts: 1079
Own Kudos [?]: 2005 [0]
Given Kudos: 200
Location: India
Concentration: Finance, Technology
GMAT 1: 730 Q49 V41
GPA: 4
Send PM
Manager
Manager
Joined: 27 Dec 2012
Posts: 110
Own Kudos [?]: 260 [0]
Given Kudos: 23
Send PM
Retired Moderator
Joined: 22 Aug 2013
Posts: 1181
Own Kudos [?]: 2552 [0]
Given Kudos: 459
Location: India
Send PM
Re: If x is an integer, is (x^2 + y^2)^(1/2) an integer? [#permalink]
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
Retired Moderator
Joined: 26 Nov 2012
Posts: 473
Own Kudos [?]: 497 [0]
Given Kudos: 46
Send PM
Re: If x is an integer, is (x^2 + y^2)^(1/2) an integer? [#permalink]
Bunuel wrote:
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


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.
Manager
Manager
Joined: 24 Dec 2016
Posts: 93
Own Kudos [?]: 45 [0]
Given Kudos: 145
Location: India
Concentration: Finance, General Management
WE:Information Technology (Computer Software)
Send PM
Re: If x is an integer, is (x^2 + y^2)^(1/2) an integer? [#permalink]
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 ?
Math Expert
Joined: 02 Sep 2009
Posts: 94421
Own Kudos [?]: 642418 [0]
Given Kudos: 86332
Send PM
Re: If x is an integer, is (x^2 + y^2)^(1/2) an integer? [#permalink]
Expert Reply
Shruti0805 wrote:
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 ?


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).
Retired Moderator
Joined: 22 Aug 2013
Posts: 1181
Own Kudos [?]: 2552 [0]
Given Kudos: 459
Location: India
Send PM
Re: If x is an integer, is (x^2 + y^2)^(1/2) an integer? [#permalink]
Shruti0805 wrote:
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.
Math Expert
Joined: 02 Sep 2009
Posts: 94421
Own Kudos [?]: 642418 [0]
Given Kudos: 86332
Send PM
Re: If x is an integer, is (x^2 + y^2)^(1/2) an integer? [#permalink]
Expert Reply
amanvermagmat wrote:
Shruti0805 wrote:
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.


I answered this here: https://gmatclub.com/forum/if-x-is-an-i ... l#p1852776
Senior Manager
Senior Manager
Joined: 21 Mar 2016
Posts: 448
Own Kudos [?]: 120 [0]
Given Kudos: 103
Send PM
Re: If x is an integer, is (x^2 + y^2)^(1/2) an integer? [#permalink]
stat1 : says x^2 = y^2
substitute in the stem,, suff,,,
given x is a integer,,

stat2 : clearly suff,,

ans D
GMAT Club Bot
Re: If x is an integer, is (x^2 + y^2)^(1/2) an integer? [#permalink]
Moderator:
Math Expert
94421 posts