If xyz

Question

If xyz < 0 and z < 0, then which of the following must be true? A. xy=1 B. xy<1 C. xy>-z D. zy0

Abhishek009 · Answer

Let z = -1 Now, xyz < 0 => -xy < 0 Or, xy > 0 , Thus, Answer must be (E)

BrentGMATPrepNow · Answer

Here's a different approach....

Given: xyz is  NEGATIVE  and z is  NEGATIVE

We know that  xyz = (xy)(z) 
Replace values to get:  NEGATIVE  = (xy)( NEGATIVE )
From this we can conclude that (xy) is POSITIVE

Answer: E

Cheers,
Brent

EgmatQuantExpert · Answer

Solution

Given  
In this question, we are given that
 • xyz < 0 and z < 0

To find  
We need to determine
 • From the given options, which one is true

Approach and Working out  
We know that 
 • x * y * z < 0
Or, x * y *   =

Now, if the product of x and y is negative, then negative * negative = positive, which is not possible
Alternatively, if the product of x and y is positive, then positive * negative = negative, which is true

Therefore, xy > 0

Thus, option E is the correct answer.

Correct Answer: Option E

Grover6481 · Answer

Hi Brent,

What if X and Y are both negative? Then none of the options would be suitable right?

BrentGMATPrepNow · Answer

If x and y are both negative, then xy = (negative)(negative) = positive. 
So, answer choice E is still correct.

bumpbot · Answer

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If xyz < 0 and z < 0, then which of the following must be true?

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