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

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Kudos [?]: 20 [0], given: 12

If a, b, and c are integers, is a - b + c greater than a + b [#permalink]  06 Feb 2012, 07:27
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25% (medium)

Question Stats:

81% (01:39) correct 19% (01:30) wrong based on 43 sessions
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
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Kudos [?]: 45136 [1] , given: 6645

Re: if a, b, and c are integers, is a - b + c greater than a+ b [#permalink]  06 Feb 2012, 07:33
1
KUDOS
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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Kudos [?]: 0 [0], given: 11

Re: If a, b, and c are integers, is a - b + c greater than a+ b [#permalink]  18 Mar 2012, 01:25
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
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Posts: 28272
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Kudos [?]: 45136 [0], given: 6645

Re: If a, b, and c are integers, is a - b + c greater than a+ b [#permalink]  18 Mar 2012, 05:42
Expert's post
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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Kudos [?]: 117 [0], given: 16

Re: If a, b, and c are integers, is a - b + c greater than a+ b [#permalink]  18 Mar 2012, 08:30
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] 18 Mar 2012, 08:30
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