In this question on inequalities, we can use some basic properties of inequalities and solve this question without too much of difficulty.
Let us try to analyse the data given in the question statement.
1) a+b>0. If the sum of two numbers is more than ZERO, there are not many conclusions we can draw from this situation about the signs of the numbers. The only things we can conclusively say are:
Both the numbers cannot be negative
Both the numbers cannot be ZERO
If a<0, b>0 in such a way that the absolute value of b is more than the absolute value of a.
If b<0, a>0 in such a way that the absolute value of a is more than the absolute value of b.
2) The second piece of information given in the question is \(a^b\)<0. This means that a is definitely negative and b is positive.
From the above, it’s clear that
statement I and II are definitely true. Based on this, answer options A and C can be eliminated.
a is negative, b is positive and a+b>0 means that the absolute value of b is definitely more than the absolute value of a i.e. |b| > |a|. Statement III is also definitely true. Answer options B and E can be eliminated
The correct answer option is D.
As you see, there weren’t too many advanced concepts we applied here. We stuck to the basics and we were able to solve it in less than 2 minutes. This is probably why there is so much emphasis on being good with your basics, regardless of the topic.
Hope that helps!
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Crackverbal Prep Team
www.crackverbal.com