Question: What is the average (arithmetic mean) annual salary of the 6 employees of a toy company?

(1) If the 6 annual salaries were ordered from least to greatest, each annual salary would be $6,300 greater than the preceding annual salary.
(2) The range of the 6 annual salaries is $31,500.

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

“What is the average (arithmetic mean) annual salary of the 6 employees”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review 2021". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation:
Approach Solution 1:
(1) If the 6 annual salaries were ordered from least to greatest, each annual salary would be $6,300 greater than the preceding annual salary.
x, x + 6300, x + 2 * 6300, x + 3 * 6300, x + 4* 6300, x + 5 * 6300
Avg = ( x + ( x + 5 * 6300 )) / 2
= ( 2x + 5 * 6300 ) / 2
No information about x

Insufficient

(2) The range of the 6 annual salaries is $31,500.
|No information about individual salary
Insufficient

Combining both :
No new information, St 2) can be derived from St 1) itself

Insufficient

Correct Answer: E

Approach Solution 2:
The average = Sum of salaries/6

Let first salary be x
The next salary will be x + 6,300 and so it goes to the 6th salary that equals x + 6,300*5
We have one variable that we don't know

Insufficient.

Statement 2)
Tells us the range X6 - X1 = 31,500
So we don't have anything specific about the salaries. Insufficient.

Now combine
The range is basically X6 - X1 = x + 6,300 *5 - x = 31,500
Basically tautology.
We don't know the value of x.

Insufficient.

Correct Answer: E

Approach Solution 3:
We don't know individual values. So insufficient.
2. We know only the ranges. Value can be anything. So insufficient
1+2 salaries are 0,6300,12600,18900,25200,31500
6300,12600,18900,25200,31500,37800

So any values possible. So insufficient

Correct Answer: E

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