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

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KSBGC
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If xyz < 0 and z < 0, then which of the following must be true? [#permalink] New post   Updated on: 20 Jan 2019, 02:17
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If xyz < 0 and z < 0, then which of the following must be true?

A. xy=1
B. xy<1
C. xy>-z
D. zy<z
E. xy>0
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E

Originally posted by KSBGC on 20 Jan 2019, 01:58.
Last edited by Bunuel on 20 Jan 2019, 02:17, edited 1 time in total.
Renamed the topic and edited the question.
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Abhishek009
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Re: If xyz < 0 and z < 0, then which of the following must be true? [#permalink] New post   20 Jan 2019, 08:43
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selim wrote:
If xyz < 0 and z < 0, then which of the following must be true?

A. xy=1
B. xy<1
C. xy>-z
D. zy<z
E. xy>0

Let z = -1

Now, xyz < 0 => -xy < 0

Or, xy > 0 , Thus, Answer must be (E)
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BrentGMATPrepNow
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Re: If xyz < 0 and z < 0, then which of the following must be true? [#permalink] New post   26 Mar 2020, 07:07
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KSBGC wrote:
If xyz < 0 and z < 0, then which of the following must be true?

A. xy=1
B. xy<1
C. xy>-z
D. zy<z
E. xy>0


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
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Re: If xyz < 0 and z < 0, then which of the following must be true? [#permalink] New post   26 Mar 2020, 07:44
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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 * [negative] = [negative]

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
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Grover6481
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Re: If xyz < 0 and z < 0, then which of the following must be true? [#permalink] New post   24 Aug 2020, 12:40
BrentGMATPrepNow wrote:
KSBGC wrote:
If xyz < 0 and z < 0, then which of the following must be true?

A. xy=1
B. xy<1
C. xy>-z
D. zy<z
E. xy>0


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


Hi Brent,

What if X and Y are both negative? Then none of the options would be suitable right?
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BrentGMATPrepNow
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Re: If xyz < 0 and z < 0, then which of the following must be true? [#permalink] New post   24 Aug 2020, 12:44
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Grover6481 wrote:
Hi Brent,

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


If x and y are both negative, then xy = (negative)(negative) = positive.
So, answer choice E is still correct.
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Re: If xyz < 0 and z < 0, then which of the following must be true? [#permalink] New post   17 Nov 2023, 11:49
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If xyz < 0 and z < 0, then which of the following must be true? [#permalink]
17 Nov 2023, 11:49
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