Data Sufficiency : Number Properties & Equations

About a third of the questions that appear on the Quantitative section of the GMAT CAT test are data sufficiency (DS) questions. Here is a DS question from Number properties and number theory. Number properties and number theory is a hot favorite when it comes to setting DS questions.

For the uninitiated amongst us, this is how the instructions to a DS question will look like.

Directions

This data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in a leap year or the meaning of the word counterclockwise), you must indicate whether –

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Numbers

All numbers used are real numbers.

Figures

A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).

Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.

You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.

All figures lie in a plane unless otherwise indicated.

Note: In data sufficiency problems that ask for the value of a quantity, the data given in the statement are sufficient only when it is possible to determine exactly one numerical value for the quantity.

Question

What is the value of b?

1) a = 3
2) (a-3)(b+2)=0

The correct answer is E. i.e., Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Explanatory Answer
Statement 1: It is obvious that statement 1 is not sufficient. Data given does not provide any information about the value of b. So, we can eliminate choices A and D. So we are down to choices B, C or E.

Statement 2: An equation with two variables ‘a’ and ‘b’. Hence, the information provided is not sufficient.

Note do not make the mistake of solving the equation as either (a – 3) = 0 or (b + 2) = 0 and decide that b = -2. What if only (a – 3) = 0 and (b + 2) was not ‘0’.

Combining the two statements, we know a = 3, so, (a – 3) = 0. But that leaves the question of what (b + 2) or what ‘b’ is unanswered.

Hence, choice E is the correct answer.

Data sufficiency questions are usually quite tricky. You can ensure success in cracking these questions only with adequate practice. Any serious aspirant should solve about 250 to 300 data sufficiency questions before taking the actual GMAT test.