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

Question

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 · Accepted Answer

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.

Answer: C.

pappueshwar · Answer

bunuel,

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

Bunuel · Answer

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.

boomtangboy · Answer

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

BrentGMATPrepNow · Answer

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

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

Take  a - b + c > a + b - c 
Subtract a from both sides to get:  -b + c > b - c 
Add b to both sides to get:  c > 2b – c 
Add c to both sides to get:  2c > 2b  
Divide both sides by 2 to get:  c > b

REPHRASED target question :    Is c > b?

Statement 1 : b is negative. 
No information about c, so there's no way to determine whether  c > b 
Since we cannot answer the  REPHRASED target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : c is positive. 
No information about b, so there's no way to determine whether  c > b 
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 b is negative
Statement 2 tells us that c is positive
So, it MUST BE THE CASE that  c > b 
Since we can answer the  REPHRASED target question  with certainty, the combined statements are SUFFICIENT

Answer = C

RELATED VIDEO
 https://www.youtube.com/watch?v=MyG1K3ee69w

jsuc79 · Answer

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 Answer = C Hi, how is the question rephrase from "If a, b, and c are integers, is a - b + c greater than a + b - c?" to "2a – b + c > a – b – 2c"? Thank you.

BrentGMATPrepNow · Answer

Yeesh - looks like I answered a totally different question

I have edited my response (above) accordingly. Cheers, Brent

Basshead · Answer

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

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

(1) b is negative

No information about c; INSUFFICIENT.

(2) c is positive

No information about b; INSUFFICIENT.

(1&2) If b is negative and c is positive, we can conclude with certainty that c < b. SUFFICIENT.

Answer is C.

bumpbot · Answer

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

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

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