Data Sufficiency

We want to know if abcd is negative. We know that a negative times a negative is a positive, so for abcd to be negative, 1 or 3 of the variables must be negative. If 0, 3, or 4 variables are negative, then abcd will be positive. (Note: if any of the variables are 0, then abcd will be 0.)

Statement 1
a < b < c < d
We have a bunch of possibilities here. All variables can be positive (e.g. 1<2<3<4). a alone can be negative (e.g. -1<2<3<4). a and b can both be negative (e.g.-2<-1<3<4). And so on. Because we can have any number of negative variables, Statement 1 is insufficient.

Statement 2
ad > 0
This tells us that either a and d are both positive, OR a and d are both negative. However, this tells us nothing about b and c. If neither or both are negative, abcd will be positive. But if only one is negative, abcd will be negative. Insufficient.

Both
If a and d are both positive and a < b < c < d, then all 4 variables are positive, and abcd is positive. If a and d are both negative and a < b < c < d, then all 4 variables are negative, and abcd is positive. So with the statements together, we know that abcd is NOT negative. Sufficient.

M7MBA wrote:Is the product abcd negative?

(1) a < b < c < d
(2) ad > 0

Target question: Is the product abcd negative?

Statement 1: a < b < c < d
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of a, b, c, and d that satisfy statement 1. Here are two:
Case a: a = -1, b = 1, c = 2 and d = 3. In this case, abcd = (-1)(1)(2)(3) = -6. So, the answer to the target question is YES, the product abcd is negative
Case b: a = -2, b = -1, c = 2 and d = 3. In this case, abcd = (-2)(-1)(2)(3) = 12. So, the answer to the target question is NO, the product abcd is not negative
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of testing values when a statement doesn't feel sufficient, read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: ad > 0
Since there's no information about b and c, there's no way to determine whether the product abcd is negative
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 2 tells us that ad > 0
This means that EITHER a and d are both negative OR a and d are both positive.
Let's examine each case separately...

Case a: a and d are both negative. We also know that a < b < c < d. We can see that d is the greatest value. So, if d is negative, then a, b and c are also negative.
So, the product abcd = (NEGATIVE)(NEGATIVE)(NEGATIVE)(NEGATIVE) = POSITIVE. So, in this case, the answer to the target question is YES, the product abcd is negative

Case b: a and d are both positive. We also know that a < b < c < d. We can see that a is the least value. So, if a is positive, then b, c and d are also positive.
So, the product abcd = (POSITIVE)(POSITIVE)(POSITIVE)(POSITIVE) = POSITIVE. So, in this case, the answer to the target question is YES, the product abcd is negative

There are only two possible cases (above), and in each case the answer to the target question is the same: YES, the product abcd is negative
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent