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# Is xyz>0?

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Senior Manager
Status: 1,750 Q's attempted and counting
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15 Nov 2013, 23:51
1
00:00

Difficulty:

55% (hard)

Question Stats:

58% (01:32) correct 42% (01:37) wrong based on 119 sessions

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Is xyz > 0 ?

(1) xy + yz > 0

(2) xz > 0

oe to follow
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Joined: 02 Sep 2009
Posts: 50623

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16 Nov 2013, 03:31
avohden wrote:
Is xyz > 0 ?

(1) xy + yz > 0

(2) xz > 0

oe to follow

Notice that both statements hold true if all unknowns are positive as well if all unknowns are negative. Now, if x, y, and z are positive then xyz > 0 but if x, y, and z are negative then xyz < 0.

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17 Nov 2013, 16:26
xyz>o
= x; y; z # 0
1- xy +yz >0
=y (x+z) >0
= either y> 0 and x+z>0 or both are < 0
Hence NOT SUFFICIENT

2- xz>0
= x >0; z>0 or both are <0
hence Not sufficient

Taking 1 and 2 together
same scenario exist Hence NOT SUFFICIENT
Ans - E
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Senior Manager
Status: 1,750 Q's attempted and counting
Affiliations: University of Florida
Joined: 09 Jul 2013
Posts: 496
Location: United States (FL)
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GMAT 1: 600 Q45 V29
GMAT 2: 590 Q35 V35
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GMAT 4: 610 Q44 V30
GPA: 3.45
WE: Accounting (Accounting)

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19 Nov 2013, 20:25

official explanation

answer E. In this Positive/Negative Number Properties problem, the question "is xyz > 0?" is really asking if any of the following are true: -All of x, y, and z are positive -Exactly two of x, y, and z are negative (with one as positive)
Those are the combinations that will lead to a positive product xyz (if one or three of the variables are negative, the product will be negative).

From statement 1, you can factor it to y(x + z) > 0, but this still allows for multiple possibilities: All could be positive, or all could be negative and the left side would look like:

Negative(Negative Sum) > 0 -----> So statement 1 is not sufficient.

For statement 2, this tells you that either:

-Both x and z are positive (which would allow for y to be either negative or positive, allowing for two different answers) or -Both x and z are negative (which would give a positive product for xyz if y were positive, or a negative product if y were negative) So statement 2 is not sufficient.

Even taking both statements together there remains a possibility of either product. If you go back to the factored inequality from statement 1: y(x + z) > 0

And incorporate what you learned from statement 2, that "x and z have the same sign":

If both x and z are positive, then y is positive and the product xyz is positive. If both x and z are negative, then y is negative and the product xyz is negative. Because both answers, positive and negative, are possible, you do not have sufficient information and the correct answer is E.

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23 Sep 2017, 04:58
Hello from the GMAT Club BumpBot!

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Re: Is xyz>0? &nbs [#permalink] 23 Sep 2017, 04:58
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# Is xyz>0?

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