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# If x, y, and z are 3 positive consecutive integers such that

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Senior Manager
Joined: 04 Nov 2006
Posts: 267
Location: California
Followers: 1

Kudos [?]: 5 [0], given: 0

If x, y, and z are 3 positive consecutive integers such that [#permalink]  20 Dec 2006, 14:32
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If x, y, and z are 3 positive consecutive integers such that x < y < z, what is the remainder when the product of x, y, and z is divided by 8?

(1) (xz)^2 is even

(2) 5 . y^3 is odd
Senior Manager
Joined: 08 Jun 2006
Posts: 343
Location: Washington DC
Followers: 1

Kudos [?]: 8 [0], given: 0

Re: DS_If x, y, and z are 3 positive consecutive... [#permalink]  20 Dec 2006, 15:35
mm007 wrote:
If x, y, and z are 3 positive consecutive integers such that x < y < z, what is the remainder when the product of x, y, and z is divided by 8?

(1) (xz)^2 is even

(2) 5 . y^3 is odd

Going for D here ... wait for OA though

From 1) possible cases - (x even, z even) or (x even, z odd) or (x odd, z even)
But from the question stem ...x < y < z , here x and z are both either even or odd.
so only even possible ..that means multiple of 8

From 2) y ^3 has to be odd..so y odd ..so x and z are even...divisible by 8
Director
Joined: 30 Nov 2006
Posts: 592
Location: Kuwait
Followers: 11

Kudos [?]: 132 [0], given: 0

I would go for D

question gives: x<y<z and x,y,z and consecutive ints.

question asks: remainder if xyz/8 ?

Statement 1 : (XZ)^ 2 is even
------------------------------------
from the question, x and z : either both even or both odd
XZ * XZ is even so XZ must be even --> x and z both are even
therefore, y is odd

since the product xyz consists of two even factors, it must be divisible by 2 and also by 4 --> it is divisible by 8

Statement 1 is sufficient

Statement 2: 5 y^3 is odd
--------------------------------
5 is odd --> y^3 must be odd
so, y also must be odd
if y is odd, then x and z are even integers
for the same reasoning in statement 1, the product xyz is divisible by 8

Statement 2 is sufficient

Director
Joined: 17 Jul 2006
Posts: 716
Followers: 1

Kudos [?]: 8 [0], given: 0

A gives the info. that x and Z are even and so Y is odd

B gives the info that Y is odd and so the other integers must be even. since they are consecutive integers.
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