GRE Quantitative Comparison: Don’t Forget to Look at BOTH Quantities

One of the pitfalls for students studying for the GRE is balancing content learning with the cultivation of appropriate test-taking strategies. If you work under the misconception that the GRE is simply testing your ability to memorize rules and formulas, then you’ll inevitably find yourself in situations where you’ll waste precious seconds (or even minutes!) solving a question that could have been answered in a much more intuitive way. Nowhere is this issue more apparent than in Quantitative Comparison (QC) questions. When doing QC questions, many students commit the cardinal sin of solving for an unknown instead of establishing the relationship. To understand what I mean, let’s look at the following example.

Bob took 50 tests. On 30 of the tests, he averaged 80, and on the other 20 tests, he averaged 90.

Quantity A: Bob’s average score for all 50 tests

Quantity B: 85

So what would an inefficient test-taker do? As soon as she sees that Quantity A is asking for Bob’s average score for all 50 tests, our inefficient test-taker will take the given information, set up the average formula three times, and solve for the average for all 50 tests. Though such an approach will certainly yield the right answer, it will be far more computation and calculation-intensive than such questions are designed to be. What mistake did our test-taker make? She didn’t look at both quantities! It’s important to understand that this question isn’t really concerned with Bob’s average on all 50 tests. Instead, it’s concerned with the relationship between Bob’s average for the 50 tests and the score of 85. That 85, though seemingly random, is put there strategically by the test-takers. When comparing an unknown to a quantity, you must understand what the relevance of that quantity is. In this case, the relevance of 85 is that it is half-way between 80 and 90. Had Bob scored 80 and 90 on an equal number of tests, his average for all of the tests would have been 85. However, from the given information, we know that he scored 80 on more tests than 90. Since Bob averaged 80 on more tests than he averaged 90, we can conclude that his average for all 50 tests was less than 85. The correct answer is thus Quantity B.

Notice that we were able to establish this relationship without doing any calculations. This is an indispensable piece of advice for quantitative comparisons. These questions are designed in such a way that the calculations required to arrive at a relationship will be minimal. But the issue is that students misconstrue the questions. Instead of trying to identify a quantitative relationship between the quantities (which often doesn’t require concrete values), they dive into calculations at the first opportunity (such as above, where our hypothetical student would calculate the average for all 50 tests). Yes, our hypothetical test-taker just answered the question correctly, but she probably spent an extra minute to get to the right answer — 60 seconds that are invaluable on a timed, adaptive test like the GRE.

If I seem passionate about all of this, it’s because I am! If you get bogged down in the details of QC questions, you’re going to significantly handicap yourself on the test. The 35-minute time-allotment reflects the test-maker’s belief that QC questions should take less time than standard multiple-choice questions. But if you don’t let this fact dictate your approach toward these questions, then you’ll inevitably find yourself strapped for time as you go through the rest of the section.