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inequality trap

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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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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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by maihuna » Tue Jan 06, 2009 2:48 pm
B is OA. thanks
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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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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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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
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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
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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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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

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by cramya » Wed Jan 07, 2009 8:12 pm
Thanks Ian and Adilka for the clarification.
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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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