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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~fluke