GRE Quantitative Comparison: Compare, Don’t Calculate!

Many students studying for the GRE make the critical mistake of viewing Quantitative Comparison questions in the same way they view Discrete Quantitative questions (these are the traditional multiple-choice questions that appear on the SAT and most other standardized tests). Both question-types obviously address your Quantitative Reasoning skills, but they do so in vastly different ways. Whereas the traditional Discrete Quantitative questions are concerned with your ability to set up what the question is asking for and to arrive at a concrete answer, Quantitative Comparison questions are concerned not with the actual value of either column, but, rather, with how the two values in the columns relate to each other. Due to the unique nature of these questions, it’s essential to step out of the problem-solving mindset that you’re accustomed to and, instead, view the questions from the top-down and assess the most efficient way to make the comparison. For easy questions, such an approach is often obvious. Let’s take a look at the question below as an example:

A                                                B

.33(978)                             .24(976)

Though you could certainly use your on-screen calculator to arrive at the exact value for each column, you’d save time by recognizing that since .33 is greater than .24 and 978 is greater than 976, the value in column A must be larger.

Okay, so pretty straightforward. Now, how do the test-makers tweak this concept? By putting values in the columns that don’t seem comparable!

Let’s look at the below as an example:

A                                      B

20⁴⁰                           2¹²⁰

This should be a bit more challenging. We know that it would be possible to calculate the value of each column, so we can definitely eliminate choice D (a comparison cannot be established), but, the on-screen GRE calculator doesn’t have exponents, so we can’t actually do out those values. So what options do we have? Well, as is almost always the case in a QC question, we should attempt to manipulate the columns to make them comparable.

Right now, the columns are each in exponential form, but the values have different bases and different exponents. Hmm, what if we make the bases look comparable. Column B can’t be broken down any further, but we could break down the base in Column A into its primes.  We can re-write 20⁴⁰ as (2² x 5)⁴⁰. Distribute the exponent, and now we have (2⁸⁰)(5⁴⁰) vs 2¹²⁰. Ok, now we’re getting somewhere. Both sides have base 2. In column A, we have 80 2’s and 40 5’s; in column B, we have 120 2’s. At this point, our comparison looks as follows:

A                                      B

2⁸⁰ 5⁴⁰                           2¹²⁰

Now, we can take advantage of the fact that both sides have an exponential term with base 2. How? You guessed it: manipulation! Divide both sides by (2⁸⁰) and you arrive at the comparison:

A                                      B

5⁴⁰                                2⁴⁰

Now, the comparison is (finally!) straightforward. We’re comparing exponential terms with the same exponent, so determine which quantity is greater, we just need to identify which quantity turns out to have the bigger base. In this case, it turns out to be Quantity A, so our answer is “A.”

Admittedly, this was an example of a fairly difficult Quantitative Comparison question, but the steps we undertook here should generalize to many situations on test day. If you’re given a comparison that appears unwieldy or impossible without a calculator, you should be thinking: Simplify!. Given the time constraints of the exam and the reasoning skills it tests, there almost always will be a method available to arrive a simpler comparison, and, as you practice more, these similarities should become more apparent.