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

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Director
Joined: 07 Jun 2004
Posts: 610

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Location: PA
If x, y, and z are 3 positive consecutive integers such that [#permalink]

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23 Sep 2006, 05:50
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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) 5y3 is odd

Kudos [?]: 923 [0], given: 22

Director
Joined: 06 May 2006
Posts: 790

Kudos [?]: 39 [0], given: 2

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23 Sep 2006, 05:58
D?

Case 1: (xz)^2 is even
=> xz is even.
From given data, x<y<z are consecutive, we can conclude that x and z should both be even numbers.
=> Remainder should be zero.

Case 2: 5*(y^3) is odd
=> y is odd.
=> From data given in the question, that x and z are even.
=> Remainder should be zero.
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Uh uh. I know what you're thinking. "Is the answer A, B, C, D or E?" Well to tell you the truth in all this excitement I kinda lost track myself. But you've gotta ask yourself one question: "Do I feel lucky?" Well, do ya, punk?

Kudos [?]: 39 [0], given: 2

SVP
Joined: 05 Jul 2006
Posts: 1750

Kudos [?]: 432 [0], given: 49

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23 Sep 2006, 10:33
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) 5y3 is odd

n,n-1,n+1 = y,x,z respectively

the prodyct is multiple of 3 and 2 (at least one is even)

from one

xz is even thus the product is divisible by 8.....suff remainder is 0

from 2

y is odd thus x,z are even one a multiple of two and the other of 4...suff remainder is zero

My answer is D

Kudos [?]: 432 [0], given: 49

Senior Manager
Joined: 11 Jul 2006
Posts: 377

Kudos [?]: 17 [0], given: 0

Location: TX
Re: DS : Crazy Eights [#permalink]

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23 Sep 2006, 19:08
1
This post was
BOOKMARKED
rxs0005 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) 5y3 is odd

Yes, it should be D

n(n+1)(n+2) for any integer n
Is divisible by 8 if n is even

A We know that x and z are even , so xyz is divisible by 8. Suff
B We know that y is odd so x and y should be even since xyz are consecutive. Suff

Kudos [?]: 17 [0], given: 0

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Posts: 16587

Kudos [?]: 273 [0], given: 0

Re: If x, y, and z are 3 positive consecutive integers such that [#permalink]

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05 Sep 2015, 10:43
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Kudos [?]: 273 [0], given: 0

Re: If x, y, and z are 3 positive consecutive integers such that   [#permalink] 05 Sep 2015, 10:43
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# If x, y, and z are 3 positive consecutive integers such that

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