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PS - Even & Odd

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PS - Even & Odd

by Xbond » Sun Oct 04, 2009 7:44 am
Hi there,

Could you help me to resolve this PS and explain the step of resolution

k and t are integers and k²-t² is an odd integer, which of the following must be an even integer ?

I. k+t+2
II. k²+2kt+t²
III. k²+t²

a) None
b) I only
c) II only
d) III only
e) I,II and III
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by cbenk121 » Sun Oct 04, 2009 8:08 pm
Here's my solution:

First, you must find out whether k and t are odd or even. This problem is all about the results of performing operations on even and odd numbers.

Given that k^2 - t^2 is an odd number, then you know that k^2 is even, and t^2 is odd. Of course, it could be reverse, but it shouldn't matter because of commutative and associative laws.

So, you then know that k must be even, and t must be odd. Even * Even = Even, and Odd * Odd = Odd.

Now, just go through the statements:

1: Even + Odd + Even = Odd
2: Even*Even + Even*Even*Odd + Odd*Odd = Even + Even + Odd = Odd
3: Even + Odd = Odd

The answer then is None.

To double check, you could just pick numbers for k and t, say 3 and 2, and then quickly evaluate the three statements.
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by Xbond » Mon Oct 05, 2009 12:49 pm
thanks
OA is A
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