Bunuel 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 negativeCase 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 negativeSince 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: http://www.gmatprepnow.com/articles/dat ... lug-values Statement 2: ad > 0Since there's no information about b and c, there's no way to determine whether
the product abcd is negativeSince 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 negativeCase 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 negativeThere are only two possible cases (above), and in each case the answer to the target question is the same:
YES, the product abcd is negativeSince we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
Thank you for a nice solution. Did you mean that the product abcd is positive not negative, right?