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

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If a + b + c > 0, is c > 2?  [#permalink]

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New post Updated on: 10 Jun 2015, 03:35
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Question Stats:

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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

Originally posted by tjerkrintjema on 10 Jun 2015, 03:04.
Last edited by Bunuel on 10 Jun 2015, 03:35, 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]

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New post 10 Jun 2015, 03:07
2
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]

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New post 10 Jun 2015, 03:42
1
2
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]

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New post 10 Jun 2015, 03:43
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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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If a + b + c > 0, is c > 2?  [#permalink]

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New post 04 Oct 2016, 17:54
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]

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New post 15 Aug 2018, 12:22
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Re: If a + b + c > 0, is c > 2? &nbs [#permalink] 15 Aug 2018, 12:22
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