Last visit was: 29 Apr 2026, 00:47 It is currently 29 Apr 2026, 00:47
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
User avatar
patrannn
User avatar
Joined: 30 Dec 2003
Last visit: 02 Feb 2010
Posts: 21
Location: Danbury
Posts: 21
Kudos: 0
If k and t are integer and k^2 - t^2 is an odd integer, 21 Apr 2008, 03:58
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If k and t are integer and k^2 - t^2 is an odd integer, which of the following must be an even integer ?

i)k+t+2
ii)k^2=2kt+t^2
iii)k^2+t^2

1)None
2)i only
3)ii only
4)iii only
5)i,ii and iii



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
alpha_plus_gamma
User avatar
Joined: 14 Aug 2007
Last visit: 17 Jun 2010
Posts: 298
Own Kudos:
641
Concentration: MC, PE, VC
Posts: 298
Kudos: 641
If k and t are integer and k^2 - t^2 is an odd integer, 21 Apr 2008, 06:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
patrannn
If k and t are integer and k^2 - t^2 is an odd integer, which of the following must be an even integer ?

i)k+t+2
ii)k^2=2kt+t^2
iii)k^2+t^2

1)None
2)i only
3)ii only
4)iii only
5)i,ii and iii
Show more

Given : (k+t)(k-t)= odd, i.e k+t=odd k-t=odd i.e either k is odd and t is even OR k is even and t is odd.

(i) k+t is odd => (k+t) + 2 => odd

(ii) (k^2 - t^2) which is odd = even (as anything multiplied by 2)...??? WTH

(iii) even square + odd square (or vice versa) = even

So Answer is 4 (iii) only
User avatar
[email protected]
User avatar
Joined: 14 Jan 2007
Last visit: 04 Feb 2009
Posts: 312
Own Kudos:
956
Posts: 312
Kudos: 956
If k and t are integer and k^2 - t^2 is an odd integer, 21 Apr 2008, 07:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
alpha_plus_gamma
patrannn
If k and t are integer and k^2 - t^2 is an odd integer, which of the following must be an even integer ?

i)k+t+2
ii)k^2=2kt+t^2
iii)k^2+t^2

1)None
2)i only
3)ii only
4)iii only
5)i,ii and iii

Given : (k+t)(k-t)= odd, i.e k+t=odd k-t=odd i.e either k is odd and t is even OR k is even and t is odd.

(i) k+t is odd => (k+t) + 2 => odd

(ii) (k^2 - t^2) which is odd = even (as anything multiplied by 2)...??? WTH

(iii) even square + odd square (or vice versa) = even

So Answer is 4 (iii) only
Show more

Even + odd is odd.

I think there is some problem with the option ii as odd can't be equal to even.
patrannn, please check the question.
i think 'none' is the answer.
User avatar
agold
User avatar
Joined: 11 Mar 2008
Last visit: 01 Mar 2009
Posts: 1,577
Own Kudos:
302
Location: Southern California
Concentration: Investment Banking
Schools:Chicago (dinged), Tuck (November), Columbia (RD)
Posts: 1,577
Kudos: 302
If k and t are integer and k^2 - t^2 is an odd integer, 21 Apr 2008, 15:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
None. Plug in k = 3, t = 2. 3^2 - 2^2 = 5 = odd. None of the options in the list will come up as even.
User avatar
alpha_plus_gamma
User avatar
Joined: 14 Aug 2007
Last visit: 17 Jun 2010
Posts: 298
Own Kudos:
641
Concentration: MC, PE, VC
Posts: 298
Kudos: 641
If k and t are integer and k^2 - t^2 is an odd integer, 21 Apr 2008, 20:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
[email protected]
alpha_plus_gamma
patrannn
If k and t are integer and k^2 - t^2 is an odd integer, which of the following must be an even integer ?

i)k+t+2
ii)k^2=2kt+t^2
iii)k^2+t^2

1)None
2)i only
3)ii only
4)iii only
5)i,ii and iii

Given : (k+t)(k-t)= odd, i.e k+t=odd k-t=odd i.e either k is odd and t is even OR k is even and t is odd.

(i) k+t is odd => (k+t) + 2 => odd

(ii) (k^2 - t^2) which is odd = even (as anything multiplied by 2)...??? WTH

(iii) even square + odd square (or vice versa) = even

So Answer is 4 (iii) only

Even + odd is odd.

I think there is some problem with the option ii as odd can't be equal to even.
patrannn, please check the question.
i think 'none' is the answer.
Show more

Thanks for pointing that out..I don't know when will I avoid such mistakes [:(]
User avatar
bkk145
User avatar
Joined: 10 Jun 2007
Last visit: 23 Feb 2014
Posts: 645
Own Kudos:
1,801
Posts: 645
Kudos: 1,801
If k and t are integer and k^2 - t^2 is an odd integer, 21 Apr 2008, 21:48
Kudos
Add Kudos
Bookmarks
Bookmark this Post
patrannn
If k and t are integer and k^2 - t^2 is an odd integer, which of the following must be an even integer ?

i)k+t+2
ii)k^2=2kt+t^2
iii)k^2+t^2

1)None
2)i only
3)ii only
4)iii only
5)i,ii and iii
Show more

The answer is None.

We know that k^2 - t^2 = odd = (k+t)*(k-t)
We also know that only
odd*odd = odd

This means:
(k+t) = odd & (k-t) = odd
Now, Eliminate "i" because odd + 2 will always be odd.

In "ii", I think this is what you mean:
k^2 - 2kt + t^2 = (k-t)*(k-t) = odd*odd = odd
Eliminate "ii"

In "iii", we need to work out the solution further...
Knowing that
(k+t) = odd
(k-t) = odd
There are two cases here:
odd + even = odd
even + odd = odd
This means k and t will never be odd&odd or even&even pair. They will always be either even&odd or odd&even. In other word, they will always be different.

This means
k^2 + t^2 = even^2 + odd^2 = odd
Eliminate "iii"
User avatar
prasannar
User avatar
Joined: 05 Jan 2008
Last visit: 23 Aug 2012
Posts: 352
Own Kudos:
4,077
Posts: 352
Kudos: 4,077
If k and t are integer and k^2 - t^2 is an odd integer, 22 Apr 2008, 00:29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
1- None

Picked by plugging numbers 3,2



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!