We'll examine a third strategy that can sometimes be the fastest and easiest approach. We'll call this the "logical approach."

To set things up, please consider the following QC question:

A. The quantity in Column A is greater

B. The quantity in Column B is greater

C. The two quantities are equal

D. The relationship cannot be determined from the information given

The algebraic approach to this question looks something like this:

First multiply both sides by

Then add

Then add

And, finally, divide both sides by

So, now we're comparing

This means the correct answer must be **A**.

Now let's take the original question and use logic to solve it (in about 5 seconds).

Column A: If ** positive**.

Column B: If ** negative**.

So, the two columns can be rewritten as:

From here, we can see that Column A is always positive and Column B is always negative. As such, Column A will always be greater than Column B. So, the correct answer is A.

Let's try another one. See if you can solve it in your head.

A. The quantity in Column A is greater

B. The quantity in Column B is greater

C. The two quantities are equal

D. The relationship cannot be determined from the information given

For this question, I'll leave the algebraic approach to you.

Let's apply some logic.

First, we're told that . In order to apply some logic, let's refer to the denominator as "something." In other words,

In other words, it must be the case that

Now consider the fact that

In other words

Now that we have concluded that

If

So, although the algebraic approach is typically the superior approach for quantitative comparison questions involving variables, be sure to take a moment to see whether the problem can be solved by applying a little logic.