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20 Dec 2021, 02:30
Kudos
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
72% (01:23) correct
28%
(01:48)
wrong
based on 76
sessions
History
Date
Time
Result
Not Attempted Yet
Is \(q < 0\) ?
(1) \(\frac{p^2}{q^3} > 0\)
(2) \(q^2-\frac{p^3}{q} < 0\)
(1) \(\frac{p^2}{q^3} > 0\)
(2) \(q^2-\frac{p^3}{q} < 0\)
20 Dec 2021, 03:23
Kudos
Bookmarks
Statement 1 -
\(\frac{p^2 }{ q^3}\) > 0
We know that \(p^2\) will be positive. Hence if \(\frac{p^2 }{ q^3}\) > 0, then q > 0
Hence sufficient.
Statement 2 -
\(q^2 - \frac{p^3 }{ q}\) < 0
\(q^2 < \frac{p^3 }{ q}\)
\(q^3 < p^3 \)
We do not know the nature of p, if p < 0, then q < 0 alternatively, if p > 0, q can be either greater or less than 0.
Hence Not sufficient.
IMO A
\(\frac{p^2 }{ q^3}\) > 0
We know that \(p^2\) will be positive. Hence if \(\frac{p^2 }{ q^3}\) > 0, then q > 0
Hence sufficient.
Statement 2 -
\(q^2 - \frac{p^3 }{ q}\) < 0
\(q^2 < \frac{p^3 }{ q}\)
\(q^3 < p^3 \)
We do not know the nature of p, if p < 0, then q < 0 alternatively, if p > 0, q can be either greater or less than 0.
Hence Not sufficient.
IMO A
20 Dec 2021, 04:17
Kudos
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Bunuel
Basically asking whether q is negative or not.
(1) \(\frac{p^2}{q^3} > 0\)
It is telling us the following things:
a)q cannot be zero because in that case the equation cannot be defined.
b)p^2 (square of a number) will always be +ve
c)The whole equation is +ve
So, q cannot be 0, it cannot be -ve because then the equation becomes -ve i.e less than 0
which points to only one thing q is +ve and there we have it.
q is positive.
Sufficient.
(2) \(q^2-\frac{p^3}{q} < 0\)[/quote]
It can be simplified to
q^3-p^3 < 0
In this case q can be both +ve, -ve or 0.
Not sufficient
A is the answer.
