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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Sat Mar 27, 2010 3:57 am

If x, y, and z are consecutive negative integers, and if x > y > z, which of the following must be a positive odd integer?
(A) x y z
(B) (x - y) (y - z)
(C) x - y z
(D) x (y + z)
(E) x + y + z

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Source: Beat The GMAT — Problem Solving | Sat Mar 27, 2010 3:57 am

eaakbari: Master | Next Rank: 500 Posts; Posts: 435; Joined: Mon Mar 15, 2010 6:15 amFollowed by: 1 member; Thanked: 32 times

by eaakbari » Sat Mar 27, 2010 4:02 am

IMO B

Last edited by eaakbari on Sat Mar 27, 2010 10:35 am, edited 1 time in total.

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Fiver: Master | Next Rank: 500 Posts; Posts: 114; Joined: Mon Sep 22, 2008 3:51 am; Thanked: 8 times; GMAT Score:680

by Fiver » Sat Mar 27, 2010 9:18 am

Choose B
It will always yeild 1 as the result.

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this_time_i_will: Master | Next Rank: 500 Posts; Posts: 268; Joined: Wed Mar 17, 2010 2:32 am; Thanked: 17 times

by this_time_i_will » Sat Mar 27, 2010 9:25 am

Fastest way would be to take examples. But, we needd to ensure that we have considered all cases.

Take (-1, -2, -3) & (-2,-3,-4).

Only B fits the bill.

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pops: Master | Next Rank: 500 Posts; Posts: 148; Joined: Tue Jun 09, 2009 11:06 pm; Thanked: 7 times

by pops » Sat Mar 27, 2010 7:42 pm

thats correct, whenever solving a question by keeping examples in place of variables (x,y,z) it is important that you take more than 1 example..
Here, for example, if you take -1,-2,-3 even D would give a positive, Odd Number... So, its better you take one more example -2,-3,-4 to arrive at conclusion !

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suryapal: Senior | Next Rank: 100 Posts; Posts: 54; Joined: Wed Mar 10, 2010 6:11 am; Thanked: 1 times

by suryapal » Sun Mar 28, 2010 5:25 am

yup its B

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akhpad: Legendary Member; Posts: 809; Joined: Wed Mar 24, 2010 10:10 pmFollowed by: 4 members; Thanked: 50 times

by akhpad » Sun Mar 28, 2010 8:46 am

as x, y and z are consecutive -ve integer

x-y = 1 and y-z = 1

(x-y)(y-z) = 1

Ans B

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rockeyb: Legendary Member; Posts: 537; Joined: Sun Jul 19, 2009 7:15 amFollowed by: 1 member; Location: Nagpur , India; Thanked: 41 times

by rockeyb » Sun Mar 28, 2010 10:22 am

An alternate approach :

We know x > y >z . And x , y and z are consecutive integers , we also know consecutive integers alternate between odd and even integers .

But we do not know which variable is odd / even .

So there can be only 2 cases .

Case 1 : y = even .
So x = odd and z = odd .

Lets look at the answer options .

(A) x y z -> Odd x Even x Odd = Even , eliminate

(B) (x - y) (y - z) -> Odd - Even = Odd , Even - Odd = Odd .
Odd x Odd = Odd .
(C) x - y z -> Odd -Even = Odd .

(D) x (y + z) -> Odd x Odd = Odd .

(E) x + y + z -> Odd + Even + Odd = Even.

So far we have B , C , D as contenders .

Lets look at Case 2 :

y = odd .

x= even and z = even .

Lets check answer options now.

(A) x y z -> even x odd x even = Even , eliminate

(B) (x - y) (y - z) -> (even-odd)(odd - even)
odd x odd = odd .
(C) x - y z -> even - Even = even .

(D) x (y + z) -> even x Odd =even.

(E) x + y + z -> Even + Odd + Even = Odd .

Only option B gives the Odd result in both the cases .

Plugging in will be much faster but some times you may forget some values .

"Know thyself" and "Nothing in excess"

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gmatmachoman: Legendary Member; Posts: 2326; Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members; Thanked: 173 times; GMAT Score:710

by gmatmachoman » Sun Mar 28, 2010 10:45 am

rockeyb wrote:An alternate approach :

We know x > y >z . And x , y and z are consecutive integers , we also know consecutive integers alternate between odd and even integers .

But we do not know which variable is odd / even .

So there can be only 2 cases .

Case 1 : y = even .
So x = odd and z = odd .

Lets look at the answer options .

(A) x y z -> Odd x Even x Odd = Even , eliminate

(B) (x - y) (y - z) -> Odd - Even = Odd , Even - Odd = Odd .
Odd x Odd = Odd .
(C) x - y z -> Odd -Even = Odd .

(D) x (y + z) -> Odd x Odd = Odd .

(E) x + y + z -> Odd + Even + Odd = Even.

So far we have B , C , D as contenders .

Lets look at Case 2 :

y = odd .

x= even and z = even .

Lets check answer options now.

(A) x y z -> even x odd x even = Even , eliminate

(B) (x - y) (y - z) -> (even-odd)(odd - even)
odd x odd = odd .
(C) x - y z -> even - Even = even .

(D) x (y + z) -> even x Odd =even.

(E) x + y + z -> Even + Odd + Even = Odd .

Only option B gives the Odd result in both the cases .

Plugging in will be much faster but some times you may forget some values .

@rockeyb

Rightly said!! I would say always try to plug in more distinct set of values to reach "conclusion".This hold true for DS also.
My inputs are 3 distinct sets.Even though it may take a extra 30-40 secs..u will certainly nail it!

R&D on GMAT algorithm:

https://www.beatthegmat.com/r-d-on-gmat- ... tml#305739

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akahuja143: Master | Next Rank: 500 Posts; Posts: 182; Joined: Mon Apr 20, 2009 7:09 pmFollowed by: 1 member; Thanked: 1 times

by akahuja143 » Sun Mar 28, 2010 11:11 am

Plugging in numbers is easier and faster on this kind of probelms...

IMO B

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