Try this GRE quantitative question on Number properties [Difficulty Level – Hard]

If (a – b)c < 0, which of the following cannot be true?
a. a < b
b. c < 0
c. |c| < 1
d. ac > bc

e. (a + b)(a – b) > 0

Here is the solution:

If (a – b)c < 0, the expression (a – b) and the variable c must have opposite signs. Let's check each answer choice: (A) UNCERTAIN: If a < b, a – b would be negative. It is possible for a – b to be negative according to the question. (B) UNCERTAIN: It is possible for c to be negative according to the question. (C) UNCERTAIN: This means that -1 < c < 1, which is possible according to the question. (D) FALSE: If we rewrite this expression, we get ac – bc > 0. Then, if we factor this, we get: (a – b)c > 0. This directly contradicts the information given in the question, which states that (a – b)c < 0. (E) UNCERTAIN: If we factor this expression, we get (a + b)(a – b) < 0. This tells us that the expressions a + b and a – b have opposite signs, which is possible according to the question. The correct answer is D.