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Math Expert V
Joined: 02 Sep 2009
Posts: 58370
Is c > 2 if a + b + c > 0 ? (1) c > a + b + 2 (2) a + b + 2 < 0  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 60% (02:13) correct 40% (02:00) wrong based on 115 sessions

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Is c > 2 if a + b + c > 0 ?

(1) c > a + b + 2

(2) a + b + 2 < 0

Kudos for a correct solution.

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Manager  Joined: 13 Apr 2015
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Concentration: General Management, Strategy
GMAT 1: 620 Q47 V28 GPA: 3.25
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Re: Is c > 2 if a + b + c > 0 ? (1) c > a + b + 2 (2) a + b + 2 < 0  [#permalink]

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2
Ans:B.
1. a + b + c > 0 .... Eq 1 (Given)

a) - a - b + c > 2 .... Eq 2,
Add Eq 1 & Eq 2 => C > 1
Not sufficient.

b) - a - b > 2 .... Eq 3

Add eq 1 & eq 3... => C > 2.

Sufficient.
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Re: Is c > 2 if a + b + c > 0 ? (1) c > a + b + 2 (2) a + b + 2 < 0  [#permalink]

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1
Is c > 2 if a + b + c > 0 ?

(1) c > a + b + 2

(2) a + b + 2 < 0

statement 1
a + b + c > 0 ----1

c > a + b + 2
c-a-b >2----2

adding 1 and 2
we get c>1 not sufficient

statement 2
a + b + 2 < 0

and a + b + c > 0 --- we subtract both of the inequality
to get c>2

B sufficient

Ans B
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Math Revolution GMAT Instructor V
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Is c > 2 if a + b + c > 0 ? (1) c > a + b + 2 (2) a + b + 2 < 0  [#permalink]

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1
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.

Is c > 2 if a + b + c > 0 ?

(1) c > a + b + 2

(2) a + b + 2 < 0

Transforming the original condition and the question, we have c>-a-b from c>2? and thus we need to know the relation between -a-b and 2. From 2), we find that a+b<-2 and a+b+c>0, therefore -c<a+b<-2, -c<-2, c>2 thus it is sufficient, and B is the answer.
In case of 1), if c = 5 then a=b=1 and the answer is yes, but if c =2 then a=b=-0.5 and the answer is no. Thus it is not sufficient.
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Originally posted by MathRevolution on 03 Sep 2015, 04:38.
Last edited by MathRevolution on 06 Sep 2015, 20:43, edited 1 time in total.
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Re: Is c > 2 if a + b + c > 0 ? (1) c > a + b + 2 (2) a + b + 2 < 0  [#permalink]

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3
In statement (1) and (2) we have a+b common and Question also have a+b
To simplify, assume a+b=x

So,the Question becomes Is c>2 if x+c>0?

Statement (1)c>x+2,Sum of x+c>0 and c>x+2 (we can sum inequalities if their signs are in the same direction):

x+c+c>0+x+2

or,c>1

Not Sufficient

Statement (2) x+2<0,Subtract x+2<0 from x+c>0 (we can subtract inequalities if their signs are in the opposite directions):

x+c-x-2>0

or, c>2

Sufficient

So the Correct Answer is B
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Manager  Joined: 10 Aug 2015
Posts: 103
Re: Is c > 2 if a + b + c > 0 ? (1) c > a + b + 2 (2) a + b + 2 < 0  [#permalink]

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Solution:

a+b+c > 0 ==> c > -(a+b) -->(1)

Statement1 : c > a + b + 2 --> (2)
Add (1) and (2), then 2c > 2 --> c > 1
Therefore, insufficent.

Statement2 : a + b + 2 < 0 ==> 2 < -(a+b) ==> -2 > a+b -->(3)
add (1) and (3),then c-2 > 0 ==> c > 2
Sufficient.

So, Option B
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Re: Is c > 2 if a + b + c > 0 ? (1) c > a + b + 2 (2) a + b + 2 < 0  [#permalink]

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