Bunuel wrote:
Tough and Tricky questions: Inequalities.
Is 0 > ab?
(1) 0 > b
(2) a = b – 6
Kudos for a correct solution. OFFICIAL SOLUTION:The easiest way to answer this question is to use the rules for positive/negative number properties. We know that the product of two numbers is only negative when one of the numbers is positive and the other is negative. If the numbers have the same sign, the product is always positive.
From Statement (1), we know that b is negative. Without knowing the sign on a, it is impossible to determine whether ab is negative. So Statement (1) is insufficient.
If we translate Statement (2) into English, we get a is 6 less than b. Since this does not tell us the sign on either a or b, we cannot answer the question. This statement is also insufficient.
Now, we combine the statements. If b is negative and a is 6 less than b, then a must also be negative, since it is less than b. This is sufficient to answer the question.Since the statements are insufficient individually, but sufficient when combined, the correct answer is choice (C).
Alternate Method (Picking Numbers):Statement (1) tells us that b is negative, so we can let b = -2. If a = 3, then ab = -6, which answers the original question affirmatively. However, if a = -3, then ab = 6. So Statement (1) is insufficient because the answer to the question could be either yes or no.
Statement (2) is also insufficient because we could substitute in two positive values for the variables, such as a = 20 and b = 26, which would make ab positive, or we could substitute in a negative and a positive value, such as a = -4 and b = 2, which would make ab negative.
However, when we combine the statements, b is negative, and any negative number minus 6 will yield another negative number, so a and b are both negative. So ab is positive, which answers the original question. Again, we see that the correct answer is choice (C).