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Difficulty:
65%
(hard)
Question Stats:
59% (02:13) correct
41%
(01:57)
wrong
based on 243
sessions
History
Date
Time
Result
Not Attempted Yet
05 Aug 2013, 05:54
Kudos
Bookmarks
Is 2ab > ab ?
or is \(2ab-ab=ab>0\)? The question asks if a,b have the same sign (and are non zero numbers).
1. \(\frac{a^4}{b^3}<-17\)
The sign of \(a^4\) is \(+\), and because the fraction is less than a negative number => \(b\) must be negative. No info about \(a\), not sufficient.
2. \((ab)^3<(ab)^4\)
or \((ab)^4-(ab)^3>0\), \((ab)^3(ab-1)>0\). The first \((ab)^3\) is positive if \(ab>0\), the second term is positive if \(ab>1\), so overall that equation is positive is \(ab>1\) or \(ab<0\). Not sufficient
(1+2) From statement 1 we know that the sign of b is -, but we cannot say anything about the sign of a (that can be positive or negative as long as the conditions of statement 2, \(ab>1\) or \(ab<0\), are respected).
Not sufficient
or is \(2ab-ab=ab>0\)? The question asks if a,b have the same sign (and are non zero numbers).
1. \(\frac{a^4}{b^3}<-17\)
The sign of \(a^4\) is \(+\), and because the fraction is less than a negative number => \(b\) must be negative. No info about \(a\), not sufficient.
2. \((ab)^3<(ab)^4\)
or \((ab)^4-(ab)^3>0\), \((ab)^3(ab-1)>0\). The first \((ab)^3\) is positive if \(ab>0\), the second term is positive if \(ab>1\), so overall that equation is positive is \(ab>1\) or \(ab<0\). Not sufficient
(1+2) From statement 1 we know that the sign of b is -, but we cannot say anything about the sign of a (that can be positive or negative as long as the conditions of statement 2, \(ab>1\) or \(ab<0\), are respected).
Not sufficient
14 Apr 2018, 03:36
Kudos
Bookmarks
summer101
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
combined
b 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
