Layering in Data Sufficiency Questions

This week, we have a follow-on article from Chris Ryan, Manhattan GMAT’s Director of Instructor and Product Development. Chris introduced the concept of “layering” to us in this article on Sentence Correction. Layering is a technique used by a test writer to make a question more difficult. Today, Chris is going to show us how layering works in data sufficiency questions.

Note: I’ve repeated the introduction from the first article below, in case some of you haven’t read that one. If you did read the first one, the first few paragraphs will be review for you.

First, ACT engages in a process called “normalization,” wherein all freshly written questions are tested by actual test takers to determine what percentage answer the questions correctly (we know these questions as “experimental” questions). If too many people answer correctly, the question may need to be toughened up. If too few people answer correctly, the question may need to be dumbed down. ACT is looking to assemble a pool of questions that covers a range of difficulty, from cakewalk to mind-bending, and the test takers help them do so.

How does ACT find these test takers? Easy. Everyone who takes the GMAT will end up answering up to 10 unscored “experimental” math questions and 10 unscored “experimental” verbal questions. These questions are interspersed with the actual, scored questions with no way to identify them as experimental.

Second, the writers at ACT have a general sense of what makes a 50th percentile question, or a 75th percentile question, or a 90th percentile question. Because each test is designed to evaluate proficiency in the same range of topics, the writers have to come up with ways to test the same concepts at different levels of difficulty. That’s where “layering” comes in.

So, in a nutshell, a simple problem is made increasingly complex by adding information to obscure the core issues. As you progress in difficulty, ACT is less interested in whether you can perform basic calculations and more interested in whether you can peel away the layers to get to the core.

For example, let’s consider the following progression in Data Sufficiency:

What is the value of x?

We have no way of knowing the value of x because (so far!) we have been given no information about it. In Data Sufficiency problems we are given 2 pieces of information (called “statements”) and asked to determine whether the statements (either individually or together) provide enough information to answer the question.

In order to answer our question (What is the value of x?), the test-writers could provide you with a very straightforward statement. For example:

x = 2

This would be absurdly easy, so the test writers have to somehow tell you that x = 2 without stating it outright. What if we had the following statement:

x=√4

A little harder, but not much. Let’s try:

x² – 4x + 4 = 0

This statement can be factored into (x – 2)(x – 2) = 0, which tells us that the value of x must be 2. This is a little tougher to decipher, but it is still not at an especially high level of GMAT difficulty. (Though there is a potential trap here: if you don’t try to factor, you might assume that a quadratic equation will give you two different answers and so you might think it’s insufficient.)

What if we were given the following statement:

x^y=y^x, where x is prime and y is even.

[Note from Stacey: try to figure this one out on your own before you continue reading!]

If y is even, then y^x must be even as well. Because x^y=y^x, it must be true that x^y is also even. If x^y is even, x itself must be even. Since x is both even and prime, it must be true that x = 2, because 2 is the only even prime.

Compare the statement x^y=y^x, where x is prime and y is even, to the statement x = 2. The statements provide the same information in the end, but one is unquestionably more difficult than the other.

In Data Sufficiency, the level of difficulty is not wholly dependent on the difficulty of the concept; it depends in part on the skill with which the test writer conceals the necessary information. As you study, you should note any questions where the information was cleverly hidden and work backwards through the levels to see how the writers were able to mislead you. Many of their tricks appear over and over in questions in the Official Guide. If you learn to spot them, you will have an enormous advantage over other test takers.

Major take-aways from Chris’s article:

1. When studying, try to figure out how the author “layered” the question stem or statement to make it more difficult. Can you write out the progression, from original language all the way to the simplest version? How did the author make this information so tricky?
2. If you can strip out the layers and get yourself to the simplest representation, then you won’t be as likely to fall into a trap on a “layered” question. (You still might fall into a trap – but you will have a much better chance of avoiding it!)

* Note to ManhattanGMAT class students: “stripping out the layers” is what we call “rephrasing” in class. :)