OAT Quantitative Reasoning: Quantitative Comparisons

In each Quantitative Comparison question in the OAT Quantitative Reasoning section, you’ll see two mathematical expressions. One is Quantity A, and the other is Quantity B. You will be asked to compare them. Some questions include additional centered information. This centered information applies to both quantities and is essential to making the comparison. Since this type of question is about the relationship between the two quantities, you won’t always need to calculate a specific value for either quantity. Therefore, you do not want to rely exclusively on the onscreen calculator to answer these questions.
Quantitative Comparison questions will look like this:

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It is a good idea to memorize the Quantitative Comparison answer choice options. This is not as difficult as it sounds. The choices are always the same. The wording and the order never vary. As you work through practice problems, the choices will become second nature to you, and you will get used to reacting to the questions without reading the four answer choices, thus saving you lots of time on Test Day.

Here’s why demonstrating two different relationships between the quantities is an important strategy: if you can demonstrate two different relationships, then choice (D) is correct. There is no need to examine the question further.
But how can this demonstration be done efficiently? A good suggestion is to look at the expression(s) containing a variable and notice the possible values of the variable given the mathematical operation involved. For example, if x can be any real number and you need to compare (x + 1)² to (x + 1), pick a value for x that will make (x + 1) a fraction between 0 and 1 and then pick a value for x that will make (x + 1) greater than 1. By choosing values for x in this way, you are basing your number choices on mathematical properties you already know: a positive fraction less than 1 becomes smaller when squared, but a number greater than 1 grows larger when squared.

Compare the value of each “piece” in each quantity. If every “piece” in one quantity is greater than a corresponding “piece” in the other quantity, and the operation involved is either addition or multiplication, then the quantity with the greater individual values will have the greater total value.

When the Quantities A and B are expressed differently, you can often make the comparison easier by changing the format of one quantity so that it looks like the other. This is a great approach when the quantities look so different that you can’t compare them directly.

If the quantities you are given seem too complex to compare immediately, look closely to see if there is an addition, subtraction, multiplication, or division operation you can perform on both quantities to make them simpler—provided you do not multiply or divide by zero or a negative number.

To avoid Quantitative Comparison traps, stay alert and don’t assume anything. If you are using a diagram to answer a question, use only information that is given or information that you know must be true based on properties or theorems. For instance, don’t assume angles are equal or lines are parallel unless it is stated or can be deduced from other information given.
A common mistake is to assume that variables represent only positive integers. As you saw when using the Picking Numbers strategy, fractions or negative numbers often show a different relationship between the quantities.

If an answer looks obvious, it may very well be a trap. Consider this situation: a question requires you to think of two integers whose product is 6. If you jump to the conclusion that 2 and 3 are the integers, you will miss several other possibilities. Not only are 1 and 6 possibilities, but there are also pairs of negative integers to consider: −2 and −3, −1 and −6.

Even if two expressions look similar, they may be mathematically different. Be especially careful with expressions involving parentheses or radicals. Although time is an important factor in taking the OAT, don’t rush to the extent that you do not apply your skills correctly.
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