**Yesterday's Data Sufficiency Question Asked:**

If *b* ≠ 0 and *a* > *b*, is *a* > *c*?

(1) a/b> c/b

(2) 5*ab* > 6*bc*

**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).**

## [0] Comments to this Article