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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