If k and t are integers...

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BlindVision: Master | Next Rank: 500 Posts; Posts: 253; Joined: Fri Dec 26, 2008 8:39 pmFollowed by: 1 member; Thanked: 8 times

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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Source: Beat The GMAT — Problem Solving | Thu Jul 02, 2009 4:35 pm

shibal: Master | Next Rank: 500 Posts; Posts: 345; Joined: Wed Mar 18, 2009 6:53 pm; Location: Sao Paulo-Brazil; Thanked: 12 times; GMAT Score:660

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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ssmiles08: Master | Next Rank: 500 Posts; Posts: 472; Joined: Sun Mar 29, 2009 6:54 pm; Thanked: 56 times

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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tohellandback: Legendary Member; Posts: 752; Joined: Sun May 17, 2009 11:04 pm; Location: Tokyo; Thanked: 81 times; GMAT Score:680

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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BlindVision: Master | Next Rank: 500 Posts; Posts: 253; Joined: Fri Dec 26, 2008 8:39 pmFollowed by: 1 member; Thanked: 8 times

by BlindVision » Thu Jul 02, 2009 6:44 pm

Hey Ssmiles, I think you meant O + E + E = O in example II.

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

Thanks 2HB for the help.

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ssmiles08: Master | Next Rank: 500 Posts; Posts: 472; Joined: Sun Mar 29, 2009 6:54 pm; Thanked: 56 times

by ssmiles08 » Thu Jul 02, 2009 7:00 pm

BlindVision wrote:Hey Ssmiles, I think you meant O + E + E = O in example II.

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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[email protected]: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Wed Jan 30, 2008 11:28 am; Thanked: 5 times

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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