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If k and t are integers...

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If k and t are integers...

by BlindVision » Thu Jul 02, 2009 4:35 pm
If k and t are integers 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

A) None

B) I only

C) II only

D) III only

E) I, II, and III

OA=A
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by shibal » Thu Jul 02, 2009 4:42 pm
pick numbers...since k^2 - t^2 is odd, k must be odd and t even...
thus, for k choose 3 and t choose 2... plug in and u'll see that it's A
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by ssmiles08 » Thu Jul 02, 2009 4:55 pm
for k^2 - t^2 to be odd: one of them needs to be odd and one of them needs to be even.

O^2 - E^2 = O

it works the same way when you add: E + O = O, with or without squaring the numbers.

I) O + E = O

II) O + E + E = O

III) O^2 + E^2 = O

therefore all three of them are odd. so it is (A)
Last edited by ssmiles08 on Thu Jul 02, 2009 6:58 pm, edited 1 time in total.
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by tohellandback » Thu Jul 02, 2009 6:38 pm
plugin number k=5,t=4
A
The powers of two are bloody impolite!!
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by BlindVision » Thu Jul 02, 2009 6:44 pm
Hey Ssmiles, I think you meant O + E + E = O in example II. :D

Thank you Ssmiles & shibal, I see the approach now!

Thanks 2HB for the help.
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by ssmiles08 » Thu Jul 02, 2009 7:00 pm
BlindVision wrote:Hey Ssmiles, I think you meant O + E + E = O in example II. :D

Thank you Ssmiles & shibal, I see the approach now!

Thanks 2HB for the help.
yes...thank you for pointing it out...i seem to typo myself about a 1000 times every post.
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by [email protected] » Thu Jul 02, 2009 11:36 pm
Plug in consecutive numbers for 'k' and 't' - will help work the question out faster.
For eg: k=6 , t= 5 ; k=7 , t=8

Regards,
N
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