If k and t are integers...

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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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 · 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)