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# If a, b, and c are integers, is a - b + c greater than a + b

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Manager
Joined: 01 Dec 2011
Posts: 65
If a, b, and c are integers, is a - b + c greater than a + b [#permalink]

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06 Feb 2012, 08:27
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76% (00:50) correct 24% (01:10) wrong based on 193 sessions

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If a, b, and c are integers, is a - b + c greater than a + b - c?

(1) b is negative
(2) c is positive
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 44373
Re: if a, b, and c are integers, is a - b + c greater than a+ b [#permalink]

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06 Feb 2012, 08:33
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Expert's post
If a, b, and c are integers, is a - b + c greater than a+ b - c?

Is $$a-b+c>a+b-c$$? --> is $$2c>2b$$? --> is $$c>b$$?

(1) b is negative. Clearly insufficient.
(2) c is positive. Clearly insufficient.

(1)+(2) $$(c=positive)>(b=negative)$$. Sufficient.

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Re: If a, b, and c are integers, is a - b + c greater than a+ b [#permalink]

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18 Mar 2012, 02:25
fiendex wrote:
If a, b, and c are integers, is a - b + c greater than a+ b - c?

1) b is negative
2) c is positive

bunuel,

how did u arrive at 2c>2b? --> is c>b?
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eshwar

Math Expert
Joined: 02 Sep 2009
Posts: 44373
Re: If a, b, and c are integers, is a - b + c greater than a+ b [#permalink]

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18 Mar 2012, 06:42
pappueshwar wrote:
fiendex wrote:
If a, b, and c are integers, is a - b + c greater than a+ b - c?

1) b is negative
2) c is positive

bunuel,

how did u arrive at 2c>2b? --> is c>b?

a-b+c>a+b-c --> rearrange and cancel a's on both sides: 2c>2b --> reduce by 2: c>b?.

Hope it's clear.
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Status: May The Force Be With Me (D-DAY 15 May 2012)
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Posts: 258
Location: India
Concentration: General Management, Entrepreneurship
Re: If a, b, and c are integers, is a - b + c greater than a+ b [#permalink]

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18 Mar 2012, 09:30
hi,

Required Proof : a-b+c>a+b-c => (since integers) 2c>2b (we are not multiplying with a negative sign hence no sign change) => c>b

Now to prove this

Statement 1 : B is negative
We dont know anything about C so Insufficient

Statement 2 : C is positive
We dont know anything about B so Insufficient

Combine : C positive & B Negative

Hence C > B

Sufficient

Hope this helps
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Re: If a, b, and c are integers, is a - b + c greater than a + b [#permalink]

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18 Jan 2018, 10:38
Expert's post
Top Contributor
fiendex wrote:
If a, b, and c are integers, is a - b + c greater than a + b - c?

(1) b is negative
(2) c is positive

Target question: Is 2a – b + c > a – b – 2c?
This is a great candidate for rephrasing the target question.

Aside: We have a video with tips on rephrasing the target question (below)

Take 2a – b + c > a – b – 2c
Add b to both sides to get: 2a + c > a – 2c
Add 2c to both sides to get: 2a + 3c > a
Subtract a from both sides to get: a + 3c > 0

REPHRASED target question: Is a + 3c > 0?

Statement 1: a is positive.
No information about c, so there's no way to determine whether a + 3c > 0

Alternatively, we can examine some conflicting cases that satisfy statement 1 (a is positive):
Case a: a = 1 and c = 1, in which case a + 3c > 0
Case b: a = 1 and c = -1, in which case a + 3c < 0
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: c is positive.
No information about c, so there's no way to determine whether a + 3c > 0

Alternatively, we can examine some conflicting cases that satisfy statement 2 (c is positive):
Case a: a = 1 and c = 1, in which case a + 3c > 0
Case b: a = -5 and c = 1, in which case a + 3c < 0
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that a is positive
Statement 2 tells us that c is positive
If a and c are both positive, then it MUST BE THE CASE that a + 3c > 0
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT

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Re: If a, b, and c are integers, is a - b + c greater than a + b   [#permalink] 18 Jan 2018, 10:38
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