SOLUTION

Is z less than 0?

(1) xy > 0 and yz < 0 --> the first inequality is useless for us since it has no z. From yz < 0 we can say that y and z have opposite sings, but we don't know the sign of y to deduce something about z. Not sufficient.

(2) x > 0. Not sufficient.

(1)+(2) From xy > 0 we can say that x and y have the same sign, and since from (2) x > 0 then y > 0 too. Now, from yz < 0 we have that y and z have opposite sings and as y > 0 then z < 0. Sufficient.

Answer: C.
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Is z < 0?

(1) xy > 0 which means
either x > 0 and y > 0
or x < 0 and y < 0

So either y > 0 or y < 0

If y > 0 and yz < 0 then z < 0
but if y < 0 and yz < 0 then z > 0

Hence Statement (1) is Not Sufficient

(2) x > 0
This statement by itself gives no information about z, so this is Not Sufficient

(1) & (2)
xy > 0 and yz < 0 and x > 0

if we take xy > 0 and x > 0 then y > 0
We also have yz < 0, as y > 0, so z < 0

So (1) & (2) together is Sufficient. Hence answer is C
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Is z less than 0?

Statement 1: xy > 0 and yz < 0.

xy > 0 means x and y have the same sign. i.e. if x>0 then y>0 and if x<0 then y<0

also, yz<0 means y and z have the opp. sign. Now since y can be either greater than 0 or less than zero, hence z can also attain two different value greater than zero when y is less than zero and less than zero when y is greater than zero.

Hence not sufficient

Statement 2 x > 0

this doesn't tell us anything about z hence not sufficient

combining statement 1 and 2 we know that both x and y are greater than zero. hence z will be less than zero. Thus sufficient.

hence C

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.
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