I used substitution;

Q: Is |a| > |b|?

(1) b < -a

b+a < 0
This equation will hold true for ;
1. a: +ve; b: -ve
2. a: -ve; b: -ve
3. a: -ve; b:+ve

Substitution;
case: I
"a" can be a very big -ve number and "b", a very small positive
a=-100
b=+5
Thus; |a|>|b|. Answer to the Q: TRUE

Converse can also be true;
case II.
"a" can be a very small +ve number and "b", a very big negative
a=+5
b=-100
Thus; |a|<|b|. Answer to the Q: FALSE

Ideally, we have proven that the statement is NOT SUFFICIENT. But, we'll see other two cases as well

case III:
"a" can be a very small -ve number and "b", a very big negative
a=-5
b=-100
Thus; |a|<|b|. Answer to the Q: FALSE

case IV:
"a" can be a very big -ve number and "b", a very small negative
a=-100
b=-5
Thus; |a|>|b|. Answer to the Q: TRUE


(2) a < 0
a: -ve

Doesn't tell us anything about b;
b can be a bigger positive or bigger negative.
Not sufficient.

Combining both the statements;
a: +ve; b: -ve --- We can count this one out as a=-ve

a: -ve; b: -ve. Here b can be a bigger negative OR b can be a smaller negative both will have opposite results. NOT SUFFICIENT.

Already proven that combining both is NOT SUFFICIENT.

a: -ve; b:+ve; "a" can be a small negative and "b", a very big postive OR "a" can be a big negative and b, a very small postive. NOT SUFFICIENT.

Ans : "E"
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This question can be very easily solved with number line approach.

Is |a| > |b|?

If we rephrase the question we'll get: on the number line does point a lie further from zero than point b? Note that we are not interested in the signs of a and b.

(1) b < -a --> b+a<0, the sum of two numbers is less than zero. Now, if both numbers are negative (to the left of zero) than their sum will obviously be less than zero, and any from these two could be further from zero, thus this statement is not sufficient.

(2) a < 0. Clearly insufficient.

(1)+(2) Example from (1) is still valid (we considered a<0 in it, so 2 is satisfied), thus even taken together statements are not sufficient.

Answer: E.
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Bunuel,
This is a very silly question. Kindly pardon me, when i approached this Q i chose (A)
b < -a is the same as -a > b which means lal > lbl right ?

And another doubt, when do u substitute values for Inequalities / Solve the inequality / use the number line. I am very naive in using the number line so .. kindly mention when to use which approach.

Thanks

@Bunuel

I have this doubt:

b<-a...let say a= -3 and b=-5, (as given b<-a..it means b is also negative.). so mod of b> mod of a...hence A is suff. ?