Hi pchun008,

I assume that this question involves exponent rules. For future reference, when posting these types of questions, you should use the following notation:

When referring to X-squared, write X^2
When referring to Y-cubed, write Y^3
Etc.

Here, were told that abcd is not equal to 0, so NONE of the variables can be 0.

We're asked if A(B^2)(C^3)(D^4) < 0? This is a YES/NO question.

Since we're not allowed to use 0, we already know that (B^2) is going to be positive and (D^4) is also going to be positive.

This question is ultimately asking "Is A(C^3) < 0?"

This question can further be "re-written" as "Is one of A or C negative?" although you might not need to take this question that far.

Fact 1: A(B^2)(C^3) < 0

Since (B^2) = positive, this Fact tells us that A(C^3) < 0, so the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

Fact 2: (B^2)(C^3)(D^4) < 0

Since (B^2) is positive and (D^4) is positive, this Fact tells us that (C^3) < 0.

However, it does not tell us anything about the value of A.
If A = negative, then the answer to the question is NO.
If A = positive, then the answer to the question is YES.
Fact 2 is INSUFFICIENT

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Hi confused13,

If we deal with the question that unknown13 posed....then we can use Number Properties to solve it.

We're told that none of the variables can = 0. We're asked Is ABCD < 0? This is a YES/NO question.

Fact 1: ABC < 0

We're not told anything about D.
If D = Positive, then ABCD < 0 and the answer to the question is YES.
if D = Negative, then ABCD > 0 and the answer to the question is NO.
Fact 1 is INSUFFICIENT.

Fact 2: BCD < 0

This is similar to what we saw in Fact 1.
We don't know anything about A.
If A = Positive, then ABCD < 0 and the answer to the question is YES.
If A = Negative, then ABCD > 0 and the answer to the question is NO.
Fact 2 is INSUFFICIENT.

Combined, we know....
Since ABC < 0, then 1 or ALL 3 of the variables are NEGATIVE
Since BCD < 0, then 1 or ALL 3 of the variables are NEGATIVE
Notice how B and C appear in BOTH inequalities....

IF....
C = Negative
A = Positive
B = Positive
D = Positive
Then the answer to the question is YES.

IF....
A = Negative
B = Positive
C = Positive
D = Negative
Then the answer to the question is NO.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich