Yesterday’s Data Sufficiency Question Asked:
If b ≠ 0 and a > b, is a > c?
(1) a/b> c/b
(2) 5ab > 6bc
Here’s the full answer and explanation. Read carefully, this is where you will learn concepts and strategies.
This is a Yes/No Data Sufficiency question. The question stem tells you that b ≠ 0 and a > b. You want to find out whether there is sufficient information to determine whether a > c. There is no information in the question stem that you can use to determine whether or not a > c, so take a look at the statements.
Both of the statements are inequalities, so it’s important to remember that when you multiply both sides of an inequality by a positive number, the direction of the inequality sign stays the same, but when you multiply both sides of an inequality by a negative number, the direction of the inequality sign is reversed. Keeping this in mind, take a look at the statements.
Begin with Statement (1), a/b > c/b . If b is positive, then multiplying both sides by b gives you a > c. But if b is negative, then multiplying both sides by b gives you a < c, since the sign of the inequality must be reversed. Therefore, Statement (1) does not tell you whether or not a is greater than c. Statement (1) is insufficient. Eliminate (A) and (D).
You can use the same logic when approaching Statement (2), 5ab > 6bc. If b is positive, then dividing both sides by b gives you 5a > 6c. If only 5 pieces of a is more than 6 pieces of c, a itself must be greater than c. However, if b is negative then dividing by b gives you 5a < 6c. In this instance a could be less than c, but it could also be greater than c. Thus, Statement (2) is insufficient. Eliminate (B).
When you put the two statements together, it is still necessary to know whether b is positive or negative in order to answer the question. Since you do not have this information, the statements taken together are insufficient and the correct answer is (E).