The given question is a challenging GMAT data sufficiency practice question. Concepts covered: Statistics - Mean, Median and Range.

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 -

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

All numbers used are real numbers.

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.

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 37: If sets A and B have n elements each, are the ranges of the two sets equal?

**Statement 1**: Both sets are symmetric about their respective means.

**Statement 2**: The median of both the sets is 50.

INR

**Statement 1**: Both sets are symmetric about their respective means.

**Approach: Counter example**

__ Example__: Set A = {1, 2, 3, 4, 5}; Range = 5 – 1 = 4

Set B = {6, 7, 8, 9, 10}; Range = 10 – 6 = 4

Answer to the question is YES.

Set B = {10, 20, 30, 40, 50}; Range = 50 – 10 = 40

Answer to the question is NO.

Counter Example exists.

We are **not able to find a CONCLUSIVE answer to the question**.

Hence, statement 1 alone is not sufficient.

__Eliminate answer options A and D__.

**Statement 2**: The median of both the sets is 50.

**Approach: Counter example**

__ Example__: Set A = {47, 48, 50, 52, 53}; Range = 53 – 47 = 6

Set B = {47, 49, 50, 51, 53}; Range = 53 – 47 = 6

Answer to the question is YES.

Set B = {40, 50, 60}; Range = 60 – 40 = 20

Answer to the question is NO.

Counter Example exists.

We are **not able to find a UNEQUIVOCAL answer to the question**.

Hence, statement 2 alone is not sufficient.

__Eliminate answer option B__.

**Statements**: **From Statement 1**: Both sets are symmetric about their respective means.

**From Statement 2**: The median of both the sets is 50.

__ Example__: Set A = {48, 50, 50, 50, 52}; Range = 4

Set B = {48, 49, 50, 51, 52}; Range = 4 Answer to the question is Yes.

Set B = {40, 50, 60}; Range = 10

Answer to the question is NO.

Counter Example exists.

Despite combining both the statements, we are not able to find a DEFINITE answer to the question.

Statement TOGETHER are NOT sufficient.

__Eliminate answer option C__.

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