inequality trap

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maihuna: Legendary Member; Posts: 1578; Joined: Sun Dec 28, 2008 1:49 amFollowed by: 9 members; Thanked: 82 times; GMAT Score:720

by maihuna » Tue Jan 06, 2009 12:34 pm

If a + b > – c, is a > 2?

(1) a + b + c > 8
(2) – a + b + c < – 4

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Source: Beat The GMAT — Data Sufficiency | Tue Jan 06, 2009 12:34 pm

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Tue Jan 06, 2009 1:55 pm

I am getting B)

Given : a+b > -c
a+b+c>0

Find: Is a > 2?

Stmt I

a+b+c > 8

a=-10000 b=2000000 c=300000000

a>2 no

a=5 b=1 c=3 a+b+c>8 a>2 YES

INSUFF

Stmt II

a+b+c>0

– a + b + c < – 4

b+c+4<a

b+c < a-4 i.e a-4 > b+c ( I )

a+b+c>0
a> -b-c ( II )

Add I and II

2a-4>0
2a > 4
a>2

SUFF
Choose B)

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maihuna: Legendary Member; Posts: 1578; Joined: Sun Dec 28, 2008 1:49 amFollowed by: 9 members; Thanked: 82 times; GMAT Score:720

by maihuna » Tue Jan 06, 2009 2:48 pm

B is OA. thanks

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adilka: Senior | Next Rank: 100 Posts; Posts: 79; Joined: Thu Oct 23, 2008 9:28 am; Location: Canada; Thanked: 1 times; GMAT Score:700

by adilka » Tue Jan 06, 2009 2:55 pm

Given: a + b > – c
Stmt II: – a + b + c < – 4

Rearrange given as a+b+c>0 and then substract Stmt II from it

2a>4
a>2

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Tue Jan 06, 2009 5:05 pm

Stmt II: – a + b + c < – 4

Rearrange given as a+b+c>0 and then substract Stmt II from it

2a>4
a>2

I know we can add inequalities facing same direction without affecting the combined inequality.

It comes out what we need to find but not sure if u can subtract inequalities facing different directio?

Thoughts anyone?

Regards,
CR

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ronniecoleman: Legendary Member; Posts: 546; Joined: Sun Nov 16, 2008 11:00 pm; Location: New Delhi , India; Thanked: 13 times

by ronniecoleman » Wed Jan 07, 2009 1:04 am

IMO B

A+ B+ C > 0

B+ C > -A ------1

B+ C+ 4 < A

Replace B+ C by -A

-A+ 4 < A

A > 2

Admission champion, Hauz khaz
011-27565856

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logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

by logitech » Wed Jan 07, 2009 1:16 am

cramya wrote:
Stmt II: – a + b + c < – 4

Rearrange given as a+b+c>0 and then substract Stmt II from it

2a>4
a>2
I know we can add inequalities facing same direction without affecting the combined inequality.

It comes out what we need to find but not sure if u can subtract inequalities facing different directio?

Thoughts anyone?

Cramya never ever perform an operation when the INEQS are facing different directions.

But if they are facing the same directions..I STILL WILL BE VERY CAREFUL!

-(-a) = +a

Regards,
CR

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

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adilka: Senior | Next Rank: 100 Posts; Posts: 79; Joined: Thu Oct 23, 2008 9:28 am; Location: Canada; Thanked: 1 times; GMAT Score:700

by adilka » Wed Jan 07, 2009 9:11 am

cramya wrote:
Stmt II: – a + b + c < – 4

Rearrange given as a+b+c>0 and then substract Stmt II from it

2a>4
a>2
I know we can add inequalities facing same direction without affecting the combined inequality.
It comes out what we need to find but not sure if u can subtract inequalities facing different directio?
Thoughts anyone?
Regards,
CR

Here is how it works:

Given: a+b+c>0
Stmt II: – a + b + c < – 4 can be rearranged as a-b-c>4 (basically, multiply by -1)
Hence:
a+b+c>0
a-b-c>4

add them together, you get 2a>4

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Wed Jan 07, 2009 10:52 am

cramya wrote:
Stmt II: – a + b + c < – 4

Rearrange given as a+b+c>0 and then substract Stmt II from it

2a>4
a>2
I know we can add inequalities facing same direction without affecting the combined inequality.

It comes out what we need to find but not sure if u can subtract inequalities facing different directio?

Thoughts anyone?

Regards,
CR

Yes, but when you subtract inequalities that face in opposite directions, you're really just doing the following:

-multiplying one of the inequalities by -1 on both sides, *reversing* the inequality (so they now face in the same direction);

-adding the two inequalities together.

I've never bothered to learn rules for subtracting inequalities, and I always do the steps above; it's the only way I feel confident about each step.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Wed Jan 07, 2009 8:12 pm

Thanks Ian and Adilka for the clarification.

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aj5105: Legendary Member; Posts: 1169; Joined: Sun Jul 06, 2008 2:34 amFollowed by: 1 member; Thanked: 25 times

by aj5105 » Sat Jan 10, 2009 12:12 am

very cool..

cramya wrote:I am getting B)

Given : a+b > -c
a+b+c>0

Find: Is a > 2?

Stmt I

a+b+c > 8

a=-10000 b=2000000 c=300000000

a>2 no

a=5 b=1 c=3 a+b+c>8 a>2 YES

INSUFF

Stmt II

a+b+c>0

– a + b + c < – 4

b+c+4<a

b+c < a-4 i.e a-4 > b+c ( I )

a+b+c>0
a> -b-c ( II )

Add I and II

2a-4>0
2a > 4
a>2

SUFF
Choose B)

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