NEW HERE? LEARN MORE
closeclose
Last visit was: 23 Apr 2024, 16:32 It is currently 23 Apr 2024, 16:32
Decision Tracker
My Rewards
New posts
New comers' posts

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

If k and t are integer and k^2 - t^2 is an odd integer,

User avatar
patrannn
Intern
Intern
Joined: 30 Dec 2003
Posts: 21
Own Kudos [?]: [0]
Given Kudos: 0
Location: Danbury
Send PM
If k and t are integer and k^2 - t^2 is an odd integer, [#permalink] New post   21 Apr 2008, 03:58
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
Senior Manager
Senior Manager
Joined: 14 Aug 2007
Posts: 300
Own Kudos [?]: 581 [0]
Given Kudos: 0
Concentration: MC, PE, VC
 Q50  V37
Send PM
Re: If k and t are integer and k^2 - t^2 is an odd integer, [#permalink] New post   21 Apr 2008, 06:17
patrannn wrote:
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
User avatar
vshaunak@gmail.com
Senior Manager
Senior Manager
Joined: 14 Jan 2007
Posts: 314
Own Kudos [?]: 901 [0]
Given Kudos: 0
Send PM
Re: If k and t are integer and k^2 - t^2 is an odd integer, [#permalink] New post   21 Apr 2008, 07:32
alpha_plus_gamma wrote:
patrannn wrote:
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.
User avatar
agold
SVP
SVP
Joined: 11 Mar 2008
Posts: 1579
Own Kudos [?]: 291 [0]
Given Kudos: 0
Location: Southern California
Concentration: Investment Banking
Schools:Chicago (dinged), Tuck (November), Columbia (RD)
Send PM
Re: If k and t are integer and k^2 - t^2 is an odd integer, [#permalink] New post   21 Apr 2008, 15:45
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
Senior Manager
Senior Manager
Joined: 14 Aug 2007
Posts: 300
Own Kudos [?]: 581 [0]
Given Kudos: 0
Concentration: MC, PE, VC
 Q50  V37
Send PM
Re: If k and t are integer and k^2 - t^2 is an odd integer, [#permalink] New post   21 Apr 2008, 20:32
vshaunak@gmail.com wrote:
alpha_plus_gamma wrote:
patrannn wrote:
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.


Thanks for pointing that out..I don't know when will I avoid such mistakes [:(]
User avatar
bkk145
Director
Director
Joined: 10 Jun 2007
Posts: 654
Own Kudos [?]: 1574 [0]
Given Kudos: 0
Send PM
Re: If k and t are integer and k^2 - t^2 is an odd integer, [#permalink] New post   21 Apr 2008, 21:48
patrannn wrote:
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


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
Senior Manager
Senior Manager
Joined: 05 Jan 2008
Posts: 354
Own Kudos [?]: 3661 [0]
Given Kudos: 0
Send PM
Re: If k and t are integer and k^2 - t^2 is an odd integer, [#permalink] New post   22 Apr 2008, 00:29
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!
GMAT Club Bot
gmatclubot
Re: If k and t are integer and k^2 - t^2 is an odd integer, [#permalink]
22 Apr 2008, 00:29
Moderator:
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions