variables in DS

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amar66: Senior | Next Rank: 100 Posts; Posts: 94; Joined: Fri Jan 14, 2011 7:44 pmFollowed by: 5 members; Location: Bangalore, India; Thanked: 2 times

by amar66 » Sat May 28, 2011 10:55 pm

If x + y + z > 0, is z > 1?
(1) z > x + y +1
(2) x + y + 1 < 0

Please explain the methodology to solve these type of questions.

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Source: Beat The GMAT — Data Sufficiency | Sat May 28, 2011 10:55 pm

irock: Senior | Next Rank: 100 Posts; Posts: 89; Joined: Mon May 09, 2011 1:05 amFollowed by: 3 members; Thanked: 1 times; GMAT Score:660

by irock » Sat May 28, 2011 11:05 pm

take 1) alone and add z both the side
=> z+ z > x + y + z +1
=> 2z > 1
=> z > .5 so not sufficient as z = .7 then no and if z =1.2 then yes

take 2) alone and add z both the side
=> x + y + z +1 < z
=> 1 < z thus sufficient.

So answer is B

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smackmartine: Legendary Member; Posts: 516; Joined: Fri Jul 31, 2009 3:22 pmFollowed by: 13 members; Thanked: 112 times

by smackmartine » Sun May 29, 2011 1:16 am

IMO B

Given x+y+z> 0
Asked : whether z>1?

1) z> x+y+1

if x = 3, y =5 , z> 3+5+1 => z> 9 ,So z>1
if x=-3 , y= -5, z> -3-5+1 => z> -7 ,So z can be -6,-5......1, 2... so z may or may not be greater than 1

Insufficient.

2) x + y + 1 < 0

also , x+y+z> 0 (given)
adding 1 on both side , we get
x+y+z+1> 1
(x + y + 1) + z >1
as (x + y + 1)<0 , for above inequality to be true z >1

because , say (x + y + 1) = -1

so (x + y + 1) + z >1 can be written as -1+z >1 => z>2 , Sufficient

So B

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun May 29, 2011 4:12 am

amar66 wrote:If x + y + z > 0, is z > 1?
(1) z > x + y +1
(2) x + y + 1 < 0

Please explain the methodology to solve these type of questions.

One approach is to link the inequalities by rephrasing them in terms of x+y.
This approach will yield an inequality in which z is the only remaining variable.

Given information: x+y+z > 0.
Isolating x+y, we get:
-z < x+y.

Statement 1: z > x + y + 1.
Isolating x+y, we get:
x+y < z-1.
Linking together -z < x+y and x+y < z-1, we get:
-z < x+y < z-1
-z < z-1
1 < 2z
z > .5.
Thus, it is possible that z<1, that z=1, or that z>1.
Insufficient.

Statement 2: x+y+1 < 0.
Isolating x+y, we get:
x+y < -1.
Linking together -z < x+y and x+y < -1, we get:
-z < x+y < -1.
-z < -1.
z > 1.
Sufficient.

The correct answer is B.

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SoCan: Senior | Next Rank: 100 Posts; Posts: 97; Joined: Sun May 15, 2011 9:19 amFollowed by: 1 member; Thanked: 18 times

by SoCan » Sun May 29, 2011 12:41 pm

This boils down to the same method irock and GMATGuru showed, but is a slightly different way to look at it. I like to add the inequalities where possible. Just make sure the sign is facing the same way. It would be even clearer if the formatting let things line up properly, but you should still be able to see it

1)
x+y+z>0
-x-y+z>1
========
2z>1, or z>.5

2)
x+y+z>0
-x-y+0>1
========
z>1, sufficient

Again, this is basically the same thing the other two approaches took, but just presents it differently.

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factor26: Senior | Next Rank: 100 Posts; Posts: 99; Joined: Sun Mar 13, 2011 12:42 pm

by factor26 » Sun May 29, 2011 10:22 pm

SoCan,

Your way seems pretty straightforward when trying to solve this problem but I had one question pertaining to your reasoning on statement 2. Looking at statement 2 it is safe to assume when you have a 0 solely on the other side of the inequality we must transfer a value to the other side so we are truly comparing two different values?

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SoCan: Senior | Next Rank: 100 Posts; Posts: 97; Joined: Sun May 15, 2011 9:19 amFollowed by: 1 member; Thanked: 18 times

by SoCan » Mon May 30, 2011 7:32 am

factor26 wrote:SoCan,

Your way seems pretty straightforward when trying to solve this problem but I had one question pertaining to your reasoning on statement 2. Looking at statement 2 it is safe to assume when you have a 0 solely on the other side of the inequality we must transfer a value to the other side so we are truly comparing two different values?

I don't know if I quite understand your question, so let me know if I'm not answering it.

You could leave the zero on the side and still add the two expressions. You'd just get
z-1>0
and you'd end up adding 1 to both sides anyway.

If you're asking about the 0 in
-x-y+0>1

I just put the zero there to emphasize that there's no z in that inequality.

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factor26: Senior | Next Rank: 100 Posts; Posts: 99; Joined: Sun Mar 13, 2011 12:42 pm

by factor26 » Mon May 30, 2011 7:54 am

@ SoCan thanks for your help. Sorry for not making the question more concise, it was a long day last yesterday

. Anyway thanks again!!

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