Is |x^7|*y^3*z^4>0 (1) xy < 0 (2) yz > 0

(1) -> either x or y is negative. since we only need to know if y is negative we do not get straight answer. insuff
(2) -> either both are negative or both are positive. since we only need to know if y is negative, we do not get a straight answer. insuff

(1/2) we got no new info. insuff.

-> E

Hi All,

It looks like everyone who's responded so far is comfortable using Number Properties to get to the correct answer. Any question that can be solved with Number Properties can also be solved by TESTing VALUES.

We're asked if |X^7|(Y^3)(Z^4) > 0. This is a YES/NO question.

Fact 1: XY < 0

This tells us that we have 1 POSITIVE and 1 NEGATIVE variable

IF....
X = 1
Y = -1
Z = 1
|1^7|[(-1)^3](1^4) = (1)(-1)(1) = -1 and the answer to the question is NO.

IF....
X = -1
Y = 1
Z = 1
|(-1)^7](1^3)(1^4) = (1)(1)(1) = 1 and the answer to the question is YES.
Fact 1 is INSUFFICIENT

Fact 2: YZ > 0

This tells us that either BOTH are positive OR BOTH are negative

IF....
X = -1
Y = 1
Z = 1
(from above), the answer to the question is YES.

IF...
X = 1
Y = -1
Z = -1
|1^7|[(-1)^3][(-1)^4] = (1)(-1)(1) = -1 and the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, we know...
XY < 0
YZ > 0

We can use our prior work (from Fact 2) to quickly deal with this last step:

IF....
X = -1
Y = 1
Z = 1
(from above), the answer to the question is YES.

IF...
X = 1
Y = -1
Z = -1
(from above) and the answer to the question is NO.
Combined, INSUFFICIENT

Final Answer:
GMAT assassins aren't born, they're made,
Rich

I have been burnt in these type of questions for NOT considering one of the numbers being = 0 so now I always start with thinking if one of them CAN be zero!
Anyway here we really need to know the sign of y AND if either one of x y or z are =0.

1) xy<0 here z can or cannot be zero. INSUFFICIENT
2) yz>0 here again x can or cannot be zero. INSUFFICIENT

Combining we know neither x y or z are zero. But together we cannot know the sign of y since it can be either sign and satisfy the requirements. So both together are also INSUFFICIENT.

Answer E.

Press kudos if you think I am right.

VERITAS PREP OFFICIAL SOLUTION:

E. Since neither the absolute value of x^7 nor the value of z^4 can be negative, the positive/negative value of |x^7|y^3z^4 will depend on the positive/negative value of y itself. (Note: the other possibility is that one of the terms could equal 0, but as you'll see with the statements that gets ruled out here)

For statement 1, xy < 0 means that either x or y (but not both) is negative. Since this means that y could be positive or y could be negative, this is not sufficient.

For statement 2, yz > 0 means that either y and z are both negative or y and z are both positive. Again, since this allows for both a positive and negative value of y, this is not sufficient.

Combining the statements, you should see that both a positive and a negative possibility both remain for y, so even together the statements are not sufficient. The correct answer is E.

In |x^7|*y^3*z^4>0

|x^7| : Always Positive as it is an absolute value
z^4 : Always Positive as any number raised to an even power is positiv
y^3 : Positive or Negative depending on y.

Hence, to find the answer if |x^7|*y^3*z^4>0, we need to find if y>0 or y<0.

Statement 1:
1) x>0 and y<0
or
2) x<0 and y>0

St 1 Insufficient alone.

Statement 2:
1) y>0 and z>0
or
2) y<0 and z<0

St 2 Insufficient alone.

Statement 1 + Statement 2:
we still get 2 cases: y>0 or y<0

St1 and St2 Insufficient when combined.

Answer: E

Hello Guys,

Why it is E) answer as properly explained earlier :

|x^7| : Always Positive as it is an absolute value, this can't be negative...
z^4 : Always Positive as any number raised to an even power is positiv
y^3 : Positive or Negative depending on y.


Statement 1:
1) x>0 and y<0
or
2) x<0 and y>0 how the outcome can be negative as the numerical of| |x^7| = positive, so xy<0 means that only the second option is valid ... I might misunderstand something ?


Statement 2:
1) y>0 and z>0
or
2) y<0 and z<0

Same here |x^7| = positive so it does not change anything when we have positive or negative of Y and Z ?

Hence i would have said D

Can someone please explain why i don't have the good reasoning ?

Thank you again for the help.

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