Step 1: Analyse Question Stem
We have to calculate if z is less than zero.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: xy > 0 and yz < 0.
The product of x and y is greater than zero; this means that x and y have the same signs.
The product of y and z is lesser than zero; this means that y and z have opposite signs.
Therefore, x and z are also of opposite signs.
However, since we do not know the exact signs of x and y, the sign of z cannot be calculated.
The data in statement 1 is insufficient to find out if z is less than zero.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.
Statement 2: x > 0
Knowing that x is a positive value is not sufficient to find whether z is negative or not.
The data in statement 2 is insufficient to find out if z is less than zero.
Statement 2 alone is insufficient. Answer option B can be eliminated.
Step 3: Analyse Statements by combining
From statement 1: x and z are of opposite signs
From statement 2: x > 0
Therefore, z < 0.
The combination of statements is sufficient to answer that z is lesser than zero.
Statements 1 and 2 together are sufficient. Answer option E can be eliminated.
The correct answer option is C.