CAT 2005 — DILR Question 4
Answer the following question based on the information given below.
A management institute was established on January 1, 2000 with 3, 4, 5, and 6 faculty members in the Marketing, Organisational Behaviour (OB), Finance, and Operations Management (OM) areas respectively, to start with. No faculty member retired or joined the institute in the first three months of the year 2000. In the next four years, the institute recruited one faculty member in each of the four areas. All these new faculty members, who joined the institute subsequently over the years, were 25 years old at the time of their joining the institute. All of them joined the institute on April 1. During these four years, one of the faculty members retired at the age of 60. The following diagram gives the area-wise average age (in terms of number of completed years) of faculty members as on April 1 of 2000, 2001, 2002, and 2003.
In which year did the new faculty member join the Finance area?
Answer & solution
- A
2000
- B
2001
2002
- D
2003
Consider this explanation that can be used to answer all the questions of this set.
In any two consecutive years that the number of faculty remains same, the average age of every area increases by 1.
Wherever we find an increase/decrease not equal to 1, we can say that the number of faculty members has changed.
Consider the area of Marketing:
The number of faculty members in Marketing in 2000 = 3
∴ Total age of faculty members in Marketing in 2000 = 3 × 49.33 = 148
In 2001, as the average has decreased, we can say that a faculty member aged 25 has been added to the area.
Thus, the new average = (148 + 3 + 25)/4 = 44
Thereafter the number of faculty remains the same.
Consider the area of OB:
The number of faculty members in 2000 = 4
The number of faculty members remains the same in 2001 and 2002. As it decreases in 2003, we can say that a faculty member has been added.
Thus the new average age = (52.5 × 4 + 4 + 25)/5 = 47.8
Consider the area of Finance:
The number of faculty members in 2000 = 5
The number of faculty members has changed in 2001.
If a new member has been added, the new average would be (50.2 × 5 + 5 + 25)/6 = 46.83, which is not true.
∴ A faculty member aged 60 has retired.
New average = (50.2 × 5 + 5 - 60)/4 = 49
In 2002, there is a change in the number of faculty members again. Here, a new member is added. New average = (49 × 4 + 4 + 25)/5 = 45
The number of faculty members remains the same in 2003.
Consider the area of OM:
Following the above logic, we can say that a faculty member gets added in 2001.
As per the explanation, one faculty member retired in 2001 and one joined in 2002. The number of members remained same in 2003.
Hence, option (c).