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If x is an integer, and k = (x – 1)(x + 2) – (x – 1)(x – 2), then whic

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If x is an integer, and k = (x – 1)(x + 2) – (x – 1)(x – 2), then whic  [#permalink]

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15 Jan 2018, 05:55
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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.

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Re: If x is an integer, and k = (x – 1)(x + 2) – (x – 1)(x – 2), then whic  [#permalink]

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15 Jan 2018, 06:03
It can be simplified to: (x-1)((x+2)-(x-2)
(X-1)(4)

So whatever the case 'K' will be even

So E

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Re: If x is an integer, and k = (x – 1)(x + 2) – (x – 1)(x – 2), then whic  [#permalink]

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15 Jan 2018, 06:09
Bunuel wrote:
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?
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Joined: 02 Aug 2009
Posts: 8004
If x is an integer, and k = (x – 1)(x + 2) – (x – 1)(x – 2), then whic  [#permalink]

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15 Jan 2018, 06:47
NandishSS wrote:
Bunuel wrote:
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

(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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If x is an integer, and k = (x – 1)(x + 2) – (x – 1)(x – 2), then whic   [#permalink] 15 Jan 2018, 06:47
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