GMAT Math: Data Sufficiency intro and basic strategy

Introduction to the Data Sufficiency question type on the GMAT.

One of the toughest question types on the GMAT is “Data Sufficiency” in the quant section. These questions, initially, tend to give my students more trouble than any other question type simply because DS questions are so unlike anything you’ve done before in school or on other standardized tests.

A typical problem opens with a question, sometimes called the “stem”. The problem then offers two “premises”, which are typically some mathematical statements related to the question. You are challenged with figuring out if the premises, when taken either individually or together, will allow you to answer the question posed.

 
Let’s take a look at a demonstrative Data Sufficiency problem:

Is |x| > 0?

1. x⁰ – 1 = 0
2. x² – 1 = 0

Your options are:

• (A) Statement 1 by itself is sufficient to answer the question.
• (B) Statement 2 by itself is sufficient to answer the question.
• (C) Both statements are required to answer the question.
• (D) Either statement by itself is sufficient to answer the question.
• (E) The two statements, even taken together, are not sufficient to answer the question.

What in the…?! I know! Where does one even begin to reason this out? Let’s see if I can shed some light on basic strategies for attacking these questions and then return to the example to see how the strategies apply in this case.

 
Basic Data Sufficiency strategy:

Let’s get away from math for a minute. (Oh, we’ll get back to it, don’t you worry.) The star of today’s DS problem is my baby nephew, Barry. The problem appears as follows:

The following toys are on a store shelf: a RED BALL, a BLUE BALL, and a BLUE TEDDY BEAR. Which of these toys does Barry want for his birthday?

Consider this question first without looking at the premises. What would you love to know to answer this question? Here’s a list you might come up with:

- What color toys does Barry prefer?
- Does Barry have a preference for balls over teddy bears?
- Does Barry like toys? (This is a sneaky one, but definitely an important consideration!)

Now let’s take a look at the question together with its premises:

The following toys are on a store shelf: a RED BALL, a BLUE BALL, and a BLUE TEDDY BEAR. Which of these toys does Barry want for his birthday?

1. Barry prefers blue toys.
2. Barry prefers teddy bears to balls.

 
If the first premise is true, we still have a ball and a teddy bear to choose from, so it, by itself, is not sufficient. The answer is not A or D.

If the second premise is true, we can answer the question. Since there is only one teddy bear on the shelf, we know he will pick it over both balls. The answer is B.

Now let’s try this approach on the math question presented above.

 
Data Sufficiency solution walk-through:

Is |x| > 0?

1. x⁰ – 1 = 0
2. x² – 1 = 0

First, what would we love to know about “|x| >  0” to answer the question? How about: “When is this expression true?” Since the absolute value of x is always positive, this expression will be true in all cases EXCEPT when x is zero. So, we would really love to know “Is x equal to zero?”. (Review this part for a minute to get comfortable with the idea – this is the secret sauce for solving DS problems effectively.)

 
We will now examine the premises to see if any of them answer the question “Is x equal to zero?”.

1. x⁰ – 1 = 0

 
Any number, including zero, raised to the power of 0 is 1, so this expression simplifies to: 1 – 1 = 0, where x can be any number, including zero. Since we don’t have a yes-or-no answer for “Is x equal to zero?”, this statement is insufficient. The answer is not A or D.
 

2. x² – 1 = 0

 
We can solve this expression by adding one to both sides to get x² = 1. Then we can take the square root of both sides, which yields: x = 1 or x = -1.
 
Alternatively, if we recognize that this expression is a difference of squares (because it is equivalent to x² – 1² = 0), we can factor it into (x+1)(x-1) = 0 and solve for x by setting each expression in parenthesis to zero.
 
According to this premise then, x is either 1 or -1, which means it is *not zero*. This is sufficient to answer the question. The answer is B.

 
I hope you found this overview helpful. With practice, you will begin to crack Data Sufficiency problems more and more quickly and accurately!