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# For consecutive integers x, y, and z, where x > y > z,

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Intern
Joined: 08 Jul 2017
Posts: 38
GMAT 1: 620 Q48 V29
For consecutive integers x, y, and z, where x > y > z,  [#permalink]

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21 Apr 2018, 02:38
00:00

Difficulty:

25% (medium)

Question Stats:

100% (01:33) correct 0% (00:00) wrong based on 10 sessions

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For consecutive integers x, y, and z, where x > y > z, which of the following CANNOT be the value of ( x2 – y2 ) ( y2 – z2)?
(A) 63
(B) 99
(C) 195
(D) 276
(E) 323

conceptually weak in this Q.

Intern
Joined: 20 Dec 2014
Posts: 36
Re: For consecutive integers x, y, and z, where x > y > z,  [#permalink]

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21 Apr 2018, 02:54
robu1 wrote:
For consecutive integers x, y, and z, where x > y > z, which of the following CANNOT be the value of ( x2 – y2 ) ( y2 – z2)?
(A) 63
(B) 99
(C) 195
(D) 276
(E) 323

conceptually weak in this Q.

As we know that x,y and z are consecutive numbers and x > y > z.
I assumed x = y - 1 and z = y + 1

now $$X^2 - Y^2 = (X+Y) (X-Y)$$
= (y-1 +y) (y-1-y)
=-(2y -1)------------------------------------------- (1)

Similarly
$$Y^2 - Z^2 = (Y-Z) (Y+Z)$$
=(y+y+1)(y-y-1)
=-(2y+1)-------------------------------------------(2)

both 1 and 2 expressions are Odd (2y is even) their product will also be odd.
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Intern
Joined: 08 Jul 2017
Posts: 38
GMAT 1: 620 Q48 V29
Re: For consecutive integers x, y, and z, where x > y > z,  [#permalink]

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21 Apr 2018, 03:07
MT1988 wrote:
robu1 wrote:
For consecutive integers x, y, and z, where x > y > z, which of the following CANNOT be the value of ( x2 – y2 ) ( y2 – z2)?
(A) 63
(B) 99
(C) 195
(D) 276
(E) 323

conceptually weak in this Q.

As we know that x,y and z are consecutive numbers and x > y > z.
I assumed x = y - 1 and z = y + 1

now $$X^2 - Y^2 = (X+Y) (X-Y)$$
= (y-1 +y) (y-1-y)
=-(2y -1)------------------------------------------- (1)

Similarly
$$Y^2 - Z^2 = (Y-Z) (Y+Z)$$
=(y+y+1)(y-y-1)
=-(2y+1)-------------------------------------------(2)

both 1 and 2 expressions are Odd (2y is even) their product will also be odd.

thankyou sir.
Math Expert
Joined: 02 Sep 2009
Posts: 58434
Re: For consecutive integers x, y, and z, where x > y > z,  [#permalink]

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21 Apr 2018, 05:07
robu1 wrote:
For consecutive integers x, y, and z, where x > y > z, which of the following CANNOT be the value of ( x2 – y2 ) ( y2 – z2)?
(A) 63
(B) 99
(C) 195
(D) 276
(E) 323

conceptually weak in this Q.

Discussed here: https://gmatclub.com/forum/for-consecut ... 25298.html
_________________
Re: For consecutive integers x, y, and z, where x > y > z,   [#permalink] 21 Apr 2018, 05:07
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