Retired Moderator
Joined: 09 Jan 2021
Posts: 576
GPA: 4
WE:Analyst (Investment Banking)
Re: If x^3y^5 > 0, and x^2z^3 <0, which of the following must be
[#permalink]
20 Feb 2021, 07:40
Solution:
\(x^3\)\(y^5\)>0
As both the power of x & y are odd, for \(x^3\)\(y^5\)>0, both x &y should have same sign i.e. either positive or negative.
\(x^2\)\(z^3\)<0
Here, \(x^2 \)is positive but \(z^3\) is negative and thus, z is negative as well.
So, we know x & y both have same sign and z is negative.
A. x>0---> x can be positive or negative not necessarily true.
B. z<0---->Yes z is negative thus this has to true
C. xy >0---->As x and y has same sign if both are negative or positive xy will always be positive. Thus, this has to be true
D. yz<0----> z=negative and y could be negative or positive and yz will change according to the value y takes
E. \(\frac{x^2}{z}\)<0----> \(x^2\) is always positive and z is negative thus \(\frac{positive}{negative}\)=negative. Thus, this has to be true.
F. xyz<0----> If x &y are positive and z is negative thus, xyz is negative & If x& y are negative still xyz is negative. Thus, this is true
IMO B, C, E, F
Hope this helps!