Is xyz 0 ? (1) xy 0 (2) yz 0

Question

Is xyz > 0 ?

(1) xy > 0
(2) yz > 0

BrentGMATPrepNow · Accepted Answer

Target question :    Is xyz > 0?

Statement 1 : xy > 0  
Since there's no information about z,  we cannot determine whether xyz > 0 . 
Since we cannot answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : yz > 0  
Since there's no information about x,  we cannot determine whether xyz > 0 . 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
Statement 1 tells us that xy > 0
There are two possible scenarios: 
 scenario 1 : x and y are both positive
 scenario 2 : x and y are both negative

Statement 2 tells us that yz > 0
There are two possible scenarios: 
 scenario 3 : y and z are both positive
 scenario 4 : y and z are both negative

So, when we consider the statements COMBINED, we see that EITHER scenarios 1 and 3 can occur, OR scenarios 2 and 4 can occur. 
Let's see what happens with each possible pair:
  Scenarios 1 and 3  : x, y, and z are all positive, in which case xyz = (POSITIVE)(POSITIVE)(POSITIVE) = POSITIVE. In other words,  xyz > 0 
  Scenarios 2 and 4  : x, y, and z are all negative, in which case xyz = (NEGATIVE)(NEGATIVE)(NEGATIVE) = NEGATIVE. In other words,  xyz < 0

Since we cannot answer the  target question  with certainty, the combined statements are NOT SUFFICIENT

Answer:  E

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Akuthiala · Answer

xyz>0 for this to be true either all are positive or only 2 or negative
Statement 1
if x and y are negative xy>0 but we don't know what z is so insufficient (-Z could make it no and +Z yes)
Statement 2
Same issue as above by not knowing X

When we combine if X and Y are negative then Z is also negative but of x and y are positive then z is positive so its insufficient

E

MathRevolution · Answer

==>In the original condition, the answer is highly likely to be E with 3 variables (x,y,z). If you do 1)&2), you get x=y=z=1 yes, and x=y=z=-1, hence no, and not suffi. Thus, the answer is E.

Answer: E

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

obliraj · Answer

St. 1: 2 cases---> x,y +ve or x,y -ve No info abt z--- not sufficient
St. 2: 2 Cases---> y,z +ve or y,z -ve No info abt x--- not sufficient
Combining-------> all 3 can be +ve all 3 can be -ve--- So both answers possible---> Not sufficient
Hence E

amanvermagmat · Answer

We want to know whether the product xyz is positive or not.

Statement 1. xy > 0. Product of xy is positive. 
Now if z is positive, product xyz will be positive, but if z is negative, product xyz will be negative. so  Insufficient .

Statement 2. yz > 0. Product of yz is positive. 
Now if x is positive, product xyz will be positive, but if x is negative, product xyz will be negative. so  Insufficient .

Combining the two statements: xy > 0 and yz > 0. So x and y have same sign (both positive or both negative) and y,z also have same sign (both positive or both negative). This means all three x,y,z have same sign (all three positive or all three negative).

Now if all three are positive, product xyz will be positive. 
But if all three are negative, product xyz will be negative. 
 Insufficient  still.

Hence  E answer

BrentGMATPrepNow · Answer

Target question :    Is xyz > 0?

Jump straight to....

Statements 1 and 2 combined    
There are several values of x and y that satisfy BOTH statements. Here are two: 
Case a: x = 1, y = 1 and z = 1, in which case xyz = (1)(1)(1) = 1.  So, xyz > 0 
Case b: x = -1, y = -1 and z = -1, in which case xyz = (-1)(-1)(-1) = -1.  So, xyz < 0 
Since we cannot answer the  target question  with certainty, the combined statements are NOT SUFFICIENT

Answer:  E

Cheers,
Brent

JeffTargetTestPrep · Answer

We need to determine whether xyz > 0.
 
Statement One Alone:
 
xy>0
 
We see that either:
 
x = negative and y = negative
 
OR 
 
x = positive and y = positive
 
However, without any information regarding z, we cannot answer the question.
 
Statement Two Alone:
 
yz > 0
 
We see that either:
 
y = negative and z = negative
 
OR 
 
y = positive and z = positive
 
However, without any information regarding x, we cannot answer the question.
 
Statements One and Two Together:
 
Using our statements together, we see:
 
When x = negative, y = negative, and z = negative, xyz is less than zero.
 
When x = positive, y = positive, and z = positive, xyz is greater than zero.
 
So, statements one and two together are not sufficient to answer the question.
 
Answer: E

MathRevolution · Answer

==> In the original condition, there are 3 variables (x,y,z) and in order to match the number of variables to the number of equations, there must be 3 equations. Since there is 1 for con 1) and 1 for con 2), E is most likely to be the answer. By solving con 1) and con 2), if x=y=z=1, yes, but if x=y=x=-1, no, hence it is not sufficient.

Therefore, the answer is E.
Answer: E

Therefore, the answer is E. 
Answer: E

bumpbot · Answer

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Is xyz > 0 ? (1) xy > 0 (2) yz > 0

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