Lesson: qc04

Quantitative Comparisons Strategies

Just as with Problem Solving, handling Quantitative Comparisons requires you to know the fundamentals of arithmetic, algebra, and geometry—no doubt about it—and that’s what the math review in the Next part of this book is about. But the test designers craft Quantitative Comparisons to gauge not just your math knowledge, but also your mental agility, flexibility, and creativity in applying it. Quantitative Comparisons are designed, for example, to measure your ability to do the following:

• See the dynamic relationships between numbers
• Recognize the easiest, quickest, or most reliable way to compare quantities
• Visualize geometric shapes and relationships between shapes

In this section of the chapter, you’ll learn some strategies and techniques that demonstrate these skills. These aren’t merely tricks and shortcuts. Your facility in applying these techniques, along with your knowledge of substantive rules of math, is exactly what the test designers are attempting to measure.

What Concept Is Being Tested?

Each Quantitative Comparison question focuses on a particular math concept. The first thing to do is look at the centered information and the expressions in the columns to determine what’s being covered. This step can often help you get a head start in making the comparison.

Example

Column A		Column B
	2x2 + 9x = 5
x		-5

Explaination

The correct answer is (D). Notice that the centered equation is quadratic, and that the two quantitative expressions essentially ask you to find the value of x. You know that quadratic equations have two roots, and this is the concept that’s probably being tested here. The two roots might be the same or they may differ.
Now you know what you need to do and why. First, rewrite the centered equation in standard form: 2x²+ 9x -5 = 0. Now, factor the trinomial expression into two binomials: (2x - 1)(x + 5) = 0. It should now be clear that there are two different roots of the equation:
1/2 and -5. Since 1/2 >-5, but -5 = -5.
The correct answer is choice (D).

There May Be an Easier Way

You shouldn’t have to perform involved calculations to make a comparison. A few simple calculations may be required, but if you’re doing a lot of number crunching or setting up and solving of equations, you’ve probably missed the mathematical principal that you’re being tested for. Put your pencil down and focus on the concept, not the process.
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