Question

Last year the average (arithmetic mean) salary of the 10 employees of Company X was $42,800. What is the average salary of the same 10 employees this year?
(1) For 8 of the 10 employees, this year’s salary is 15 percent greater than last year’s salary. 
(2) For 2 of the 10 employees, this year’s salary is the same as last year’s salary.

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• D. EACH statement ALONE is sufficient.
• E. Statements (1) and (2) TOGETHER are not sufficient

Hint:

When calculating averages, use the formula for the sum of the values and apply any percentages to find the new values.

Answer 1

The Correct Option is C

Step 1: Analyze statement (1).
Statement (1) tells us that for 8 of the 10 employees, this year’s salary is 15 percent greater than last year’s salary. The total salary of these 8 employees is: \[ 8 \times 42,800 \times 1.15 = 8 \times 49,220 = 393,760 \] We are not given any information about the salaries of the remaining 2 employees, so statement (1) alone is insufficient.
Step 2: Analyze statement (2).
Statement (2) tells us that for 2 of the 10 employees, this year’s salary is the same as last year’s salary. This does not provide enough information about the other 8 employees, so statement (2) alone is insufficient.
Step 3: Combine both statements.
From statement (1), we know the total salary for 8 employees this year, and from statement (2), we know that for 2 employees, the salary remains the same. Let \( S \) be the total salary of these 2 employees this year. The total salary for all 10 employees is: \[ 393,760 + S \] The average salary is then: \[ \frac{393,760 + S}{10} \] Since \( S = 2 \times 42,800 = 85,600 \), the total salary for all 10 employees this year is: \[ 393,760 + 85,600 = 479,360 \] Thus, the average salary is: \[ \frac{479,360}{10} = 47,936 \] \[ \boxed{47,936} \]