# GMAT Data Sufficiency Practice Question 28

###### Statistics | Progressions and Range | Data Sufficiency

The given question is a challenging GMAT data sufficiency question testing concepts in Statistics. Concepts include Progressions 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 -

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.
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 28: What is the range of 3 positive integers a, b, and c ?

Statement 1: 21a = 9b = 7c
Statement 2: a + 8, b, and c, in that order are in AP.

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### Explanatory Answer | GMAT Statistics & Progressions Practice Question

#### Step 1: Evaluate Statement 1 ALONE

Statement 1: 21a = 9b = 7c

Let 21a = 9b = 7c = n
Because a, b, and c are positive integers, 'n' is a common multiple of 21, 9, and 7.
The least value for 'n' is the LCM of 21, 9, and 7 = 63.
So, 'n' is a multiple of 63 or n = 63k.
So, a = 3k, b = 7k and c = 9k. The range of the numbers is 9k – 3k = 6k

Without knowing the value of k we cannot find the range of the 3 numbers.
Hence, statement 1 is not sufficient.
Eliminate answer option A and D.

#### Step 2: Evaluate Statement 2 ALONE

Statement 2: a + 8, b, and c, in that order are in AP.

Approach : Counter example
Example : a = 1, b = 10, and c = 11. a + 8 = 9
So, 9, 10, 11 are in AP. Range = 11 - 1 = 10
Counter Example : a = 1, b = 11, c = 13. a + 8 = 9
So, 9, 11, 13 are in AP. Range = 13 - 1 = 12
Counter example exists.

We are not able to find a UNIQUE value for the range using Statement 2.
Hence, statement 2 is not sufficient.

#### Step 4: Evaluate Statements TOGETHER

Statements: Statement 1: 21a = 9b = 7c
Statement 2: a + 8, b, and c in that order are in AP.

Key inferences:
From statement 1: we know a = 3k, b = 7k and c = 9k
From statement 2: we know c - b = b - (a + 8) (because a + 8, b, and c are in AP) ... (1)
Substiute c = 9k, b = 7k and a = 3k in equation (1)
So, 9k - 7k = 7k - (3k + 8)
2k = 4k - 8
or k = 4
Therefore, the range (9k - 3k) = 6k = 6(4) = 24

We are able to find a UNIQUE value for range using the statements together.
Statements together are sufficient.

##### Choice C is the correct answer.

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