duahsolo wrote:

The average (arithmetic mean) salary in a firm increased by 20% after a number of new employees were hired. How many people joined the firm?

(1) The average (arithmetic mean) salary for those who just joined the firm is 40% higher than the average of salaries in the firm before the new employees were hired.

(2) There were 10 people in the firm initially.

We can let the number of original employees = D and the number of new employees = N. We can also let the average salary of the original employees = a and the average salary of the new employees = s.

We are given that the average (arithmetic mean) salary in the firm increased by 20% after a number of new employees were hired. Thus, the new average salary is 1.2a. However, in terms of a, s, D, and N, the new average salary is (aD + sN)/(D + N). Thus 1.2a = (aD + sN)/(D + N). We must determine the value of N.

Statement One Alone:The average (arithmetic mean) salary for those who just joined the firm is 40% higher than the average of salaries in the firm before the new employees were hired.

This means s = 1.4a. So the equation 1.2a = (aD + sN)/(D + N) becomes 1.2a = (aD + (1.4a)N)/(D + N). We can simplify this equation by dividing both sides of the equation by a, and we have:

1.2 = (D + 1.4N)/(D + N)

However, since we don’t know the value of D, we can’t determine the value of N. Statement one alone is not sufficient to answer the question.

Statement Two Alone:There were 10 people in the firm initially.

Since D = 10, the equation 1.2a = (aD + sN)/(D + N) becomes:

1.2a = (10a + sN)/(10 + N)

However, since we don’t know the values of a and s, we can’t determine the value of N. Statement two alone is not sufficient.

Statements One and Two Together:Using the information from statements one and two, we know that:

1.2 = (D + 1.4N)/(D + N) and D = 10.

Thus:

1.2 = (10 + 1.4N)/(10 + N)

1.2(10 + N) = 10 + 1.4N

12 + 1.2N = 10 + 1.4N

2 = 0.2N

N = 2/0.2 = 20/2 = 10

Answer: C

_________________

Scott Woodbury-Stewart

Founder and CEO

GMAT Quant Self-Study Course

500+ lessons 3000+ practice problems 800+ HD solutions