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If a + b + c > 0, is c > 2?

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tjerkrintjema
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If a + b + c > 0, is c > 2? [#permalink] New post   Updated on: 10 Jun 2015, 04:35
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If a + b + c > 0, is c > 2?

(1) c - a > b + 2
(2) a + b + 3 < 0

Source Mindful GMAT
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Official Answer
B

Originally posted by tjerkrintjema on 10 Jun 2015, 04:04.
Last edited by Bunuel on 10 Jun 2015, 04:35, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Re: If a + b + c > 0, is c > 2? [#permalink] New post   10 Jun 2015, 04:07
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Okay I'm not sure about the answer,

But looking at statement 1

a+b+c > 0
c-a > b+ 2
-------------+
b+2c > b+2
2c > 2
c > 1

Therefore not sufficient as it can be 2 as well

Statement 2

a+b+c > 0
a+b+3 < 0

Divide the bottom equation by -1 to switch signs

So
a+b+c > 0
-a-b-3 > 0
------------+
c-3 > 0
c > 3

Therefore I believe answer should be B.
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Re: If a + b + c > 0, is c > 2? [#permalink] New post   10 Jun 2015, 04:42
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tjerkrintjema wrote:
If a + b + c > 0, is c > 2?

(1) c - a > b + 2
(2) a + b + 3 < 0

Source Mindful GMAT


In the stem and in both statements we have a + b (in (1) c - a > b + 2 is the same as c > a + b + 2). To simplify, denote a + b as x.

If x + c > 0, is c > 2?

(1) c > x + 2. Sum 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)
c > 1.

Not sufficient.

(2) x + 3 < 0. Subtract x + 3 < 0 from x + c > 0 (we can subtract inequalities if their signs are in the opposite directions):
(x + c) - (x + 3) > 0 - 0.
c > 3.

Sufficient.

Answer: B.

Hope it's clear.
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If a + b + c > 0, is c > 2? [#permalink] New post   10 Jun 2015, 04:43
Expert Reply
Bunuel wrote:
tjerkrintjema wrote:
If a + b + c > 0, is c > 2?

(1) c - a > b + 2
(2) a + b + 3 < 0

Source Mindful GMAT


In the stem and in both statements we have a + b (in (1) c - a > b + 2 is the same as c > a + b + 2). To simplify, denote a + b as x.

If x + c > 0, is c > 2?

(1) c > x + 2. Sum 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)
c > 1.

Not sufficient.

(2) x + 3 < 0. Subtract x + 3 < 0 from x + c > 0 (we can subtract inequalities if their signs are in the opposite directions):
(x + c) - (x + 3) > 0 - 0.
c > 3.

Sufficient.

Answer: B.

Hope it's clear.


How to manipulate inequalities (adding, subtracting, squaring etc.).
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If a + b + c > 0, is c > 2? [#permalink] New post   04 Oct 2016, 18:54
tjerkrintjema wrote:
If a + b + c > 0, is c > 2?

(1) c - a > b + 2
(2) a + b + 3 < 0

Source Mindful GMAT


1: c-a > b + 2....
(a + b) = "x"
c>x+2....and x+c>0....
Sum: x+2 + c > 0 + x + c
2c>2
c>1 Insufficient

2: a + b + 3 < 0
a + b<-3....if their sum is less than -3 then c must be greater than 2 in order to fulfill the given: a + b + c> 0

B: statement 1 is insufficient but statement 2 is sufficient
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Re: If a + b + c > 0, is c > 2? [#permalink] New post   27 Aug 2019, 06:04
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Re: If a + b + c > 0, is c > 2? [#permalink]
27 Aug 2019, 06:04
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Bunuel
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