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Bunuel
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NandishSS
Bunuel
If x is an integer, and k = (x – 1)(x + 2) – (x – 1)(x – 2), then which of the following must be true?

(A) k is odd only when x is odd.
(B) k is odd only when x is even.
(C) k is even only when x is even.
(D) k is even only when x is odd.
(E) None of the above.

Simplify the equation

k = (x – 1)(x + 2) – (x – 1)(x – 2) ==>(x-1)[(x+2)-(x-2)] ==>(x-1)4

Here irrespective of x, k will be even

For x=4 , k=12

For x=3, K=8

Hence E

Bunuel, chetan2u Is it right?


Hi
Your approach is absolutely correct

(x-1)(x+2) will always be even as ONE of the two x-1 or x+2 will be odd and other even.
similarly for (x – 1)(x – 2)..

k = (x – 1)(x + 2) – (x – 1)(x – 2)= Even - Even = Even
always even
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