Data Sufficiency

Data Sufficiency questions test quantitative reasoning ability through an unusual set of directions. Generally, data sufficiency problems require much less calculating (and sometimes no calculating) than do multiple-choice problems, but they are trickier.

A math problem can be presented in many formats, such as, multiple-choice, problem solving, quantitative comparison, etc. Data Sufficiency is just one such format. But there is much to learn about the format. The discussion originates from the peculiar set of directions for the format, which we will discuss shortly. For now, it’s important to know that this format is trickier than all the other formats because it involves both logic and math. Because of the involvement of logic, many general strategies come into the picture. All these general strategies are discussed in detail in this chapter and the next. By the end of the second chapter, you will be well versed in the Data Sufficiency format. But unless you have very strong math skills, you might still find these problems challenging. The remaining chapters of the book focus on general math skills.

Note:Multiple-choice problems are about solving, while Data Sufficiency problems are generally limited to determining whether a solution exists. So, in Data Sufficiency problems, we usually skip the step of actually solving the problem. We will see that this advantage makes Data Sufficiency problems easier.

Directions and Reference Material

The directions for Data Sufficiency questions are rather complicated. Before reading any further, take some time to learn the directions cold. Some of the wording in the directions below has been changed from the Exam to make it clearer. You should never have to look at the instructions during the test.

Directions:Each of the following Data Sufficiency problems contains a question followed by two statements, numbered (1) and (2). You need not solve the problem; rather you must decide whether the information given is sufficient to solve the problem. The correct answer to a question is

A if statement (1) ALONE is sufficient to answer the question but statement (2) alone is not sufficient;
B if statement (2) ALONE is sufficient to answer the question but statement (1) alone is not sufficient;
C if the two statements TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient;
D if EACH statement ALONE is sufficient to answer the question;
E if the two statements TAKEN TOGETHER are still NOT sufficient to answer the question.

Numbers: Only real numbers are used. That is, there are no complex numbers. Drawings: A figure accompanying a data sufficiency question will conform to the information given in the question, but may conflict with the information given in statements (1) and (2). You can assume that a line that appears straight is straight and that angle measures cannot be zero.

You can assume that the relative positions of points, angles, and objects are as shown. All drawings lie in a plane unless stated otherwise.

Sample Questions

Question: 1

Is CAB a code word in Language Q?
(1) ABC is the base word.
(2) If C immediately follows B, then C can be moved to the front of the code word to generate another word.

Question: 2

How many marbles are in bowl S?
(1) If 1/4 of the marbles were removed, the bowl would be filled to 1/2 of its capacity.
(2) If 100 marbles were added, the bowl would be full.

Question: 3

For any increase in x, the value of y decreases by double the value. Also, for any decrease in x, the value of y increases by double the value. What is the value of x when y is 2?
(1) When x is 1, y = 5.
(2) When x is 3, y = 1.

Answers: 1 :C 2: C 3: D

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