12 Minute Test: Bar Graphs | Logical Reasoning (LR) and Data Interpretation (DI) - CAT PDF Download

In the table, 'n' represents the number of faculty members in different areas and 'a' represents the average age of faculty members.

Sum of ages of Naresh and Devesh in 2000 = (52 + 49) years = 101 years
In 2000, age of the third faculty member = (49.33 × 3 - 101) years = 47 years
In 2005, age of the third faculty member = (47 + 5) years = 52 years

In the table, 'n' represents the number of faculty members in different departments and 'a' represents the average age of faculty members.

• It is given that 1 person was recruited in each of the departments. This is the key sentence.
• There is a dip in average age twice only in Finance. Whenever a person joins or leaves, the average age would be disturbed from its normal increasing value of 1 every year.
• Now, as 2 persons have not joined the same department, it must only be in Finance that a person retired in 1 year and another member joined in another year.
• Because of the fact that all departments have 1 dip in their average age, and Finance has 2, the possibility that the person who retired at 60 years of age and a new faculty member joined in the same department in the same year is ruled out.
• Furthermore, the normal trend in average age in each department is an increase of 1, which would be the normal behaviour if no person joins in or leaves, unless and until the average age of persons who leave and join in the same year is exactly the same.

Furthermore, as the trend is decrease in age and it is happening only once in each of the departments except Finance, the possibility that the average age would increase when a person joins is ruled out as only 1 person joins in the entire period in the data set.

It is given that 1 person was recruited in each of the departments. This is the key sentence.

There is a dip in average age twice only in Finance. Whenever a person joins or leaves, the average age would be disturbed from its normal increasing value of 1 every year.

Now, as 2 persons have not joined the same department, it must only be in Finance that a person retired in 1 year and another member joined in another year. Because of the fact that all departments have 1 dip in their average age, and Finance has 2, the possibility that the person who retired at 60 years of age and a new faculty member joined in the same year is ruled out.

Furthermore, the normal trend in average age in each department is an increase of 1, which would be the normal behaviour if no person joins in or leaves, unless and until the average age of persons who leave and join in the same year is exactly the same.
Furthermore, as the trend is decrease in age and it is happening only once in each of the departments except Finance, the possibility that the average age would increase when a person joins is ruled out as only 1 person joins in the entire period in the data set.

Now, let us assume that the person who retired at the age of 60 years from the Finance department, retired in the period 2^nd April, 2000 - 31^st March, 2001, both dates inclusive. So, the average age of the faculty members as on 1^st April, 2001, should be (50.2 × 5 + 5 - 60)/4) years = 49 years, which matches perfectly with the data given.

Thus, the person that retired must have done so in the period given.

Now, there is a dip in the average age of faculty of the Finance department in the year 2002.

So, let us now evaluate if it matches with the data given.

If a person of 25 years of age joins the Finance department on 1^st April, 2002, then the average age of the faculty members on 1^st April, 2002 is ((49 × 4 + 4 + 25)/5) years = 45 years, which matches perfectly with the given data.

Thus, the person who joined the Finance department did so in the year 2002.
Hence, answer option 3 is correct.