The GRE section devoted to math goes by the mouthy word “Quantitative.” Half of the problems in this section are regular multiple-choice problems, but the other half are presented in a format known as Quantitative Comparison (QC for short).

QC Problems

The directions for Quantitative Comparisons look something like this:

Directions: Column A and Column B will have one quantity each. Your goal is to compare the quantities in each column and choose

1. if the quantity in Column A is greater
2. if the quantity in Column B is greater
3. if the two quantities are equal
4. if the relationship between the two quantities cannot be determined from the information given

Here’s a wildly simple example of a QC problem.

Column A		Column B
	b = 2
b		1

You have two columns, A and B, and there is a “quantity” underneath each one. This quantity might be a variable (like Column A), a number (like Column B), or some mixture of the two with a little extra thrown in for good measure. On occasion, floating above this columnar stew is some additional information that applies to the quantity in both columns, like “b = 2.”

Like the example above, the items in the two columns often can’t be compared to one another, because they are in different formats. In our example, one column has a variable while the other has a number. You would need to convert the variable into a number in order to compare them. Since the centered information states b = 2, you know that the quantity, or value, of the letter b in Column A is 2. Under Column B, the value is 1. There are no other possible interpretations or solutions using the centered information. We know that 1 is less than 2, so the correct answer must be (A).

Note the qualifying phrase “There are no other possibile interpretations or solutions” in the previous sentence. Exploring alternate possible answers is critical on QC problems, because there are often hidden outcomes that can affect the answer on a problem. Here’s a QC problem that looks similar to the previous one.

Column A		Column B
	b2 = 4
b		1

Again, you want to convert Column A into a number so you can compare it to the number in Column B. The obvious answer is that b = 2, since (2)(2) = 4. This would mean (A) is the answer . . . if there are no other possibilities, that is. In this case, you should see that b could also equal -2, since (-2)(-2) = 4. If you compare -2 with Column B’s 1, Column B’s quantity is larger, so (B) is the answer in this scenario.

One possible value for b gives you the answer (A), while another gives you an answer of (B). Whenever you have a conflict like this, the correct response is choice (D), “the answer cannot be determined by the information given.” A more precise statement for choice (D) would be that “more than one answer can be determined, and there’s no way to tell which answer is correct.” It’s not that you can’t determine an answer, it’s just that you don’t know which answer is correct.

To properly explore all possibilities on QC problems involving variables, don’t just use easy numbers like 2, 3, and 4 when giving values to variables. Be sure to insert some weird numbers like those on the following list:

On our second sample question, realizing the existence of -2 (the weird negative number) led us to the correct answer of (D).

Many incorrect QC answers are chosen in the name of speed, as people look at a problem and “see” the answer that must be the correct one. If the answer is so obvious, why not pick it quickly and zip on to the next question? The response to this hypothetical question is that answers that look correct are often traps designed to catch those who do not actually work the problem.

QC Approach Checklist

1. For the answer choices, the word always is critical. You can only pick (A) if the quantity in Column A is always greater, and you can only pick (B) if Column B’s quantity is always greater. Choice (C) is the answer if the two columns are always equal, no matter what weird numbers are punched in. Whenever you find a QC problem that has more than one possible outcome, (A), (B) and/or (C), you have (D) as your answer.



2. The goal is to compare the two problems, so you should take information and try to rearrange it in a way that makes comparison easier. If you have a problem with a lot of variables, you should realize the goal will be to get comparable variables into both columns. If one column only has numbers in it, the key to that problem is finding a way to convert the other column into a number than can be compared.



3. When variables are involved, don’t be content to plug in one value for the variable and then use that as the result. Use a “weird” number to challenge your initial finding. If you find a weird number that leads to a different result, you know the correct choice on that problem is (D).



4. Many QC problems are designed to look like there is one obvious answer. Never jump to this answer unless you have done all of the actual math that the problem demands. The obvious answer is often an incorrect choice set there to trap hurried test-takers.

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