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Bunuel
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Rishbha
chetan2u
Is \(ab > 0\)? Are a and b of SAME sign?

(1) \(\frac{1}{a}<1\)
a could be any integer except 1 and 0, so a can be positive or negative.

(2) \(b^3c^2>0\)
c^2 will always be positive, so b is positive.
Nothing about a

Combined
b>0, but a could be anything

E
Hello chetan2u,

please help me understand below query :

if 1/a< 1 , then doesnt that mean a>1 ? When we cross multiply?

And if a>1 and b>0, then even if they are fractions, the result of ab should always be gretaer than 0?

Thank you

No it doesn’t mean a>1 as you do not know the sign of a.
Say a=-2, then 1/(-2)<1 does not mean 1<1*(-2).
Yes a>1 and b>0 will always give you ab>0, but you can say anything about a
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Is \(ab > 0\)? Are a and b of SAME sign?

(1) \(\frac{1}{a}<1\)
a could be any integer except 1 and 0, so a can be positive or negative.

(2) \(b^3c^2>0\)
c^2 will always be positive, so b is positive.
Nothing about a

Combined
b>0, but a could be anything

E
Hello chetan2u,

please help me understand below query :

if 1/a< 1 , then doesnt that mean a>1 ? When we cross multiply?

And if a>1 and b>0, then even if they are fractions, the result of ab should always be gretaer than 0?

Thank you

No it doesn’t mean a>1 as you do not know the sign of a.
Say a=-2, then 1/(-2)<1 does not mean 1<1*(-2).
Yes a>1 and b>0 will always give you ab>0, but you can say anything about a


Thank you so much, I understand it now.
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