littlewarthog wrote:
Statement (1): From the information given, we can conclude that both, a and b are not negative. The two absolute values must be positive (the question stem tells us they are not 0), so a + b must also be positive. As the absolute values have the same sign, a and be must also have the same sign, otherwise their sum would not be equal to the sum of their absolute values.
Picking a few number pairs, we quickly realize that that information is sufficient. This also makes sense theoretically. Going from \(\frac{1}{a}\) to \(\frac{1}{(a+b)}\) will always decrease the term for positive a and b, while going from \(\frac{1}{a}\) to \(\frac{1}{a}+\frac{1}{b}\) will always increase the term.
So statement 1 is sufficient.
Statement (2): Here we can easily show that this is not sufficient by picking numbers. Choose e.g. 2 and 2,so we get \(\frac{1}{4}<1\), which is obviously true. But picking 2 and -1 will give \(1<\frac{1}{2}-1\), which is obviously wrong.
Therefore, answer A is correct.
1) a and B has to be positive forIaI+IbI=a+b to be correct .
so any posive value will satisfy the question.
sufficient.
2) a>b
consider both to be positive in 1st case and negative in 2nd case ,we get different answers.
a=2 & b=1 .then yes.
a=-2 & b=-3 then no.
Not sufficient.
Ans A.