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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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New post 15 Jan 2018, 04:55
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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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New post 15 Jan 2018, 05:03
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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New post 15 Jan 2018, 05:09
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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If x is an integer, and k = (x – 1)(x + 2) – (x – 1)(x – 2), then whic  [#permalink]

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New post 15 Jan 2018, 05:47
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
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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