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If b is positive, is ab positive?

1. \(a^2b>0\)


Since we are given b is positive,
if a is either positive or negative, the expression \(a^2b>0\) holds true.
Case 1: a=-3, b=2 Here, ab is negative
Case 2: a=3, b=2 Here, ab is positive(Insufficient)

2. \(a^2+b=13\)


Since we are given b is positive,
if a is either positive or negative, the expression \(a^2+b=13\) holds true.
Case 1: a=-3, b=5 Here, ab is negative
Case 2: a=3, b=5 Here, ab is positive(Insufficient)

Even combining both the statements, we will be left with two options
in the first one - both a and b are positive
in the second one - a is negative and b is positive. (Insufficient)(Option E)
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given b>0
1) (a^2).b>0 from this b>0 then a can be positive as well as negative, so sign of axb can't be determined. A,D ruled out
2) (a^2)+b=13 , b>0 and b <13 a can have Positive and Negative values, also if b>13 , then a is not defined hence sign of axb can't be determined. B ruled out.

Combining both ,
a^2+b = 13 and (a^2) x b > 0 cant solve the problem with the sign from above 2 statements, a can be negative as well as positive since its square will always be positive and therefore C ruled out

Answer is E
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+1 E

a^2*b>0
a can be both positive and negative

a^2 + b = 13
a can be both positive and negative

Even combining both we do not get if a is positive or negative
Hence E
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St:1 says nothing but what is given in question. B is positive. A can be -ve as well as +ve.Insufficient
St:2 says that a2 will be positive .Again A can be -ve as well as +ve.Insufficient

Combining does not help either. Therefore E.
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Silly Mistake, I did -> assumed that a is positive in place b - marked option D that is incorrect :(
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