summer101 wrote:
Is 2ab > ab ?
(1) \(\frac{a^4}{b^3}<-17\)
(2) \((ab)^3<(ab)^4\)
Q is "is \(2ab>ab........2ab-ab>0.........ab>0\)?"
when will this happen?
when both a and b are of SAME sign.
let's see the statements..(1) \(\frac{a^4}{b^3}<-17\)
Now \(a^4\) is positive but
a could be anything as it has EVEN power..b is surely negative..if a is negative ans is YES, if b is 0 or positive, ans is NO..
insuff
(2) \((ab)^3<(ab)^4\).....
\((ab)^3<(ab)^4..........(ab)^4-(ab)^3>0......(ab)^3(ab-1)>0\)
we can easily see from \((ab)^4-(ab)^3>0\), ab could be positive or negative..
otherwise \((ab)^3(ab-1)>0\) gives two cases..
(i) ab>0, ab-1>0 or ab>1
(ii) ab<0, ab-1<0 or ab<1.....
so ab>1 or ab<0
insuff
combinedb is negative but ab>1, then a<0 and ans is YES
b is negative but ab<0, then a is positive and ans is NO
Insuff
E
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