Data-Sufficiency questions in the GMAT test measure a candidate's proficiency in the same priciples and areas of Math that are measured by the GMAT problem solving questions.

However, the pattern and specific nature of the data sufficiency questions are designed to measure your ability to:

• analyze a quantitative problem and recognize which information is relevant and
• determine what information is sufficient to solve a given problem

This is how a Sample Data Sufficiency Question in GMAT looks 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 —

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
3. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
4. EACH statement ALONE is sufficient to answer the question asked.
5. 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
Is x = y, given that x and y are non-zero numbers?
I. (x - 25)² = (y - 25)²
II. x/y = y/x

Correct Answer
Correct answer is choice (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.

Explanatory Answer
The question asks us to evaluate if x = y.

Statement I
From statement 1, we know that (x - 25)² = (y - 25)².
This could have two possible situations. One that x = y. The second one is possible when let us say x takes the value of 50 and y takes the value of '0'. i.e., x is not equal to y. As we are not able to conclusively decide if x is equal to y or not, statement I alone is not sufficient.

We can therefore, rule out answer choices A and D. The answer has to be one of B, C or E.

Statement II
From statement II, we can conclude that x² = y².
This translates to x² - y² = 0 or (x + y)(x - y) = 0
or at least one of (x + y) or (x - y) = 0
or x = -y or x = y.
From statement II also we are not able to conclusively decide if x is equal to y. Therefore, statement II alone is not sufficient.
We can eliminate choice B also. So, the answer has to be either C or E.

If we combine the information in both the statements, this is how the expansion of the first statement will look
x² - 50x + 625 = y² - 50x + 625
or x² - 50x = y² - 50y
From statement II, we know that x² = y².
Therefore, x² - 50x = y² - 50y can be simplified as -50x = -50y
or x = y.

As we can conclude that x = y using information in both the statements, the correct answer is choice (C).