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Bunuel
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1. a+3 > b-1
Try a = 3 and b = 2
6 > 1
So a > b
Try another negative case a = -4 and b = -1
-1 > -2
But -4 < -1 . So a < b.

Hence the options A and D shall be eliminated.

2. a > |b|
Try a = 3 ; b = 2
Its true. a>b

Try a= 4 and b = -3
4>3

So option B is enough
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Statement 1 is insufficient
Lets look at statement 2
a>|b|
that means a is always greater than b
for ex take b=-3
then a>|-3| i.e a > 3
so a >b

another case
b=3
then a>|3| i.e a > 3
so a >b
answer is B
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St 1: a+3>b-1 or a-b>-4. if a-b is negative a<b and if a-b is positive, a>b. INSUFFICIENT

St 2: a>|b|. therefore a>b and a>-b too. ANSWER

Option B
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"Infer - a > b ?

S-1) b < a+4. b =2 and a = 1 a < b or b = 1 and a = 2, a > b. NS
S-2) a > |b| means a > +b and a > -b. Sufficient

Answer is B"
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