Hi,
I have taken the following approach to solve this question. Please correct me if I am wrong.
question: Is a>0?
We can solve this question by Picking numbers.
Let us consider the statements.
Statement 1:-
\(ab=25\)
Product of two numbers can be 25 in multiple ways:-
\( a*b=25\)
\( 1*25=25\) , here a > 0
\( (-1)*(-25)=25\), here a <0
So here we are not getting a definite answer regarding whether a > 0 or not.
So we can eliminate options A and D.
Statement 2:-
\(\sqrt{b} > 1\)
Squaring both sides, we get
\(b > 1\)
Here we don't have any information about a.
So we can eliminate option B.
Considering statements 1 & 2 together,
From statement 1 we know that \(a*b=25\)
now since the product is positive, so both a & b should be of same sign i.e either both a & b positive or both a & b negative and neither of them is 0.
From statement 2, we get that b is positive, so a should also be positive.
So on considering both the statements together we can definitely say that a>0.
Hence, option C is correct.