GRE Quantitative Practice Questions — Complex Multiple-choice Format
If a > 0 > b > c, and if |a| > |c|, which of the following inequalities holds in all cases?
Indicate all such inequalities.
Answer and Analysis
The correct answer is (B) and (C). (You would gain credit for answering the question correctly only by selecting both of these choices.) Here's an analysis of the three answer choices:
(A) Since b and c are both negative (less than zero in value), their product must be a positive number. But whether that product is greater than a depends on the specific values of the three numbers. For example, if b = –1, c = –2 and a = 3, then bc – a < 0. But if b = –2, c = –3 and a = 4, then bc – a > 0. These two examples suffice to show that inequality (A) does not hold in all cases.
(B) The product of a (a positive number) and b (a negative number) must be negative (less than zero). Adding c (a negative number) to that product always yields a negative number further to the left on the number line. Inequality (B) holds in all cases.
(C) Given that |a| > |c| and that a is positive while c is negative, the product of a and c must be less than b (left of b on the number line). Inequality (C) holds in all cases.