Question: In a certain office, 50 percent of the employees are college graduates and 60 percent of the employees are over 40 years old. If 30 percent of those over 40 have master's degrees, how many of the employees over 40 have master's degrees?

(1) Exactly 100 of the employees are college graduates.
(2) Of the employees 40 years old or less, 25 percent have master's degrees.

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.

“In a certain office, 50 percent of the employees are college” is a topic of the GMAT Quantitative reasoning section of GMAT. The GMAT Data Sufficiency questions consist of a problem statement and two factual statements. This specific GMAT data sufficiency question estimates the candidates’ skill in analyzing the problem and solving it with their mathematical knowledge. The most challenging part of these questions arises from smart wording that is overlooked by the candidates. The GMAT Quant section contains 31 MCQs to be completed within 62 minutes. The GMAT data sufficiency comprises 15 questions which are two-fifths of the 31 GMAT quant questions.

Solution and Explanation:

Approach Solution 1:

The problem statement informs that:

Given:

• 50 percent of the employees are college graduates
• 60 percent of the employees are over 40 years old
• 30 percent of those over 40 have master's degrees

Find Out:

• The number of employees over 40 having master's degrees

Let the total number of employees in the office be x
Therefore, as per the question, college graduates = 0.5x
Employees over 40 years old = 0.6x
Employees over 40 having master’s degrees= 0.3*0.6x

1. The statement suggests that 100 of the employees are college graduates.

Therefore, we can conclude that
0.5x = 100
Therefore, x= 200
Thus from this statement, we can discover the value of x and hence we can determine the value of 0.3*0.6x.
Thus, the number of employees over 40 having master’s degrees = 0.3* 0.6* 200 = 36
Therefore the statement alone is sufficient to get the value of the number of employees over 40 having master's degrees.

2. The statement indicates that among the employees 40 years old or less, 25 percent have master’s degrees. Therefore, there is no such information given specifically about the number of employees in any group. Only the percentage of employees is given.

Thus, the statement alone is not sufficient to find the value of employees over 40 having master’s degrees.

Correct Answer: A

Approach Solution 2:

The problem statement declares that:

Given:

• 50 percent of the employees are college graduates
• 60 percent of the employees are over 40 years old
• 30 percent of those over 40 have master's degrees

Find Out:

• The number of employees over 40 having master's degrees

According to the question, 30% of the employees over 40 years old have master's degrees. It is given that 60 percent of the employees are over 40 years old.
Therefore, we can say that 30% of 60% of total employees have master's degrees = 18% of the total employees have master’s degrees.

Therefore, the problem statement asks to find the value of this 18% of the total employees.

1. The statement states that 100 employees are college graduates.

It is given that 50% of the total employees are college graduates. Therefore, 50% of the total is equal to 100.
This gives the total number of employees present in the company.
Therefore, it would help us to give the value of 18% of total employees.
Thus statement (1) alone is sufficient to find the number of employees over 40 having master's degrees.

1. Statement (2) implies that of the employees with 40years old or less, 25% have master's degrees.

Therefore, the statement gives only the percentage information. It is required to provide one actual value to obtain the number of employees who are 40+ years old and have master’s degrees. Without any actual number, it is not possible to find the value of employees over 40 having master's degrees.

Thus statement (2) alone is insufficient to find the value of employees.

Correct Answer: A

Approach Solution 3:

The problem statement claims that:

Given:

• 50 percent of the employees are college graduates
• 60 percent of the employees are over 40 years old
• 30 percent of those over 40 have master's degrees

Find Out:

• The number of employees over 40 having master's degrees

We need to find the value of E and therefore, we are dealing with one variable. One equation is required to correspond to the number of variables and equation.

1. Since 100 employees are college graduates and it is given that 50% of employees are college graduates, therefore, we get:

50E = 100
Therefore, E=2
As per the question, 30% of 60% of employees over 40 have master's degrees = 18E over 40 have master’s degrees.
Therefore, 18E= 18*2 = 36
Thus the statement alone is sufficient.

2. In statement (2), “Of the employees 40 years old or less, 25 percent have master's degrees” we can say,

40E*25% = 10E = x
But it is not possible for us to find the value of E. Therefore, the condition in this statement alone is not sufficient.

Correct Answer: A

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