Is a − b 0? (1) a 2b (2) b a + 3

Question

Is a − b > 0?

(1) a > 2b
(2) b > a + 3

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GMATinsight · Answer

Is a-b > 0

Question: Is a > b?

Statement 1 : a > 2b

@b = 1, a = 3 YES
@b =-1 a= -1 NO

NOT SUFFICIENT

Statement 2 : b > a + 3

i.e. b is 3 units to teh right of a on Number line

i.e. b is definitely greater than a  NO

SUFFICIENT

Answer: Option B

yashikaaggarwal · Answer

To find: Is a − b > 0?

(1) a > 2b
Case 1: A & B are negative
Then -2 > -4
-2 -(-2) = 0

Case 2: A & B are positive
Then 12 > 8
12 -(8) > 0
(Insufficient)

(2) b > a + 3
Case 1: A & B are negative
Then -2 > -6+3
-6 -(-2) < 0

Case 2: A & B are positive
Then 12 > 7+3
7 -(12) < 0

B is greater than a in all cases (Sufficient)

Answer is B

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sambitspm · Answer

Kindly see the attachment.

Time: 1:06
IMO B

GMATWhizTeam · Answer

Solution Step 1: Analyse Question Stem • We need to find out if a – b > 0 Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE Statement 1: a > 2b • According to this statement: a > 2b ⟹ a – b > b • However, we don’t know if a and b are positive or negative. So, we cannot be sure if a – b > 0. For example consider the following cases: o Case 1: If a = 5 and b = 2 then, a – b > b i.e. (5 – 2 = 3) > 2  In this case, a – b = 3 which is greater than 0 o Case 2 : If a = -5 and b = -3, then a – b > b i.e. (-5 –(-3) =-2) > -3  However, in this case a – b = -2 , which is less than 0. Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D. Statement 2: b > a +3 • According to this statement: b > a + 3 ⟹ b – a > 3 ⟹ (a – b ) < -3 o Thus, we can be sure that (a – b) < 0 Hence, statement 2 is sufficient. Thus, the correct answer is Option B.

Deepender · Answer

1. not sufficient for negative values
2.it is sufficient for both positive and negative values of a

RaghavKhanna · Answer

To check: a - b > 0
i.e; a > b

St. 1:
a > 2b
(i) a and are positive integers: if a > 2b
=> a > b
(ii) a and b are negative integers: if a > 2b
=> a > b or a < b
eg: a = -5, b = -3
=> -5 > -6 but -5 < -3

St. 1 is insufficient

St. 2:
b > a +3
=> a - b < -3
=> a - b < 0

St. 2 is insufficient

Answer: B

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Is a − b > 0? (1) a > 2b (2) b > a + 3

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