CAT 2022 Slot 3 DILR Question & Solution
Data Set
In the following, a year corresponds to 1st of January of that year.
A study to determine the mortality rate for a disease began in 1980. The study chose 1000 males and 1000 females and followed them for forty years or until they died, whichever came first. The 1000 males chosen in 1980 consisted of 250 each of ages 10 to less than 20, 20 to less than 30, 30 to less than 40, and 40 to less than 50. The 1000 females chosen in 1980 also consisted of 250 each of ages 10 to less than 20, 20 to less than 30, 30 to less than 40,and 40 to less than 50.
The four figures below depict the age profile of those among the 2000 individuals who were still alive in 1990, 2000, 2010, and 2020. The blue bars in each figure represent the number of males in each age group at that point in time, while the pink bars represent the number of females in each age group at that point in time. The numbers next to the bars give the exact numbers being represented by the bars. For example, we know that 230 males among those tracked and who were alive in 1990 were aged between 20 and 30.
Question 1
In 2000, what was the ratio of the number of dead males to dead females among those being tracked?
Solution:
The total number of male and female test cases in 1980 = 1000
The total number of males alive in 2000 = 180 + 205 + 160 + 100 = 645
Thus, the number of dead males in 2000 = 1000 - 645 = 355
Similarly, the total number of dead females in 2000 = 1000 - (210 + 175 + 150 + 120) = 1000 - 655 = 345
Thus, the required ratio = 355 : 345 = 71 : 69.
Thus, the correct option is A.
Question 2
How many people who were being tracked and who were between 30 and 40 years of age in 1980 survived until 2010?
Solution:
The total number of male and female test cases in 1980 = 1000
The total number of males in the age group of 30-40(in 1980) alive till 2010 = 90
The total number of females in the age group of 30-40(in 1980) alive till 2010 = 100
Thus, the total number of people in the age group of 30-40(in 1980) alive till 2010 = 90 + 100 = 190
Thus, the correct option is C.
Question 3
How many individuals who were being tracked and who were less than 30 years of age in 1980 survived until 2020?
Solution:
The total number of male and female test cases in 1980 = 1000
The total number of males less than 30 years (in 1980) survived until 2020 = 140 + 125 = 265
The total number of females less than 30 years (in 1980) survived until 2020 = 100 + 105 = 205
Thus, The total number of people less than 30 years (in 1980) survived until 2020 = 205 + 265 = 470
Thus, the correct option is C.
Question 4
How many of the males who were being tracked and who were between 20 and 30 years of age in 1980 died in the period 2000 to 2010?
Solution:
The total number of male and female test cases in 1980 = 1000
The total number of males between 20 and 30 years of age in 1980 who died in 2000 = 205
The total number of males between 20 and 30 years of age in 1980 who died in 2010 = 165
Thus, the total number of males between 20 and 30 years of age in 1980 who died in the period 2000 to 2010 = 205 - 165 = 40
Question 5
How many of the females who were being tracked and who were between 20 and 30 years of age in 1980 died between the ages of 50 and 60?
Solution:
The total number of male and female test cases in 1980 = 1000
We are given that there are 250 females from age 20-30 in 1980 and in 2000 these females age are from 40-50 but only 175 are alive in 2000.
In 2000 there were 175 females from age 40-50. If we assume that out of these, 30 females were of age 48 years in 2000 and they died in 2005, then there are 30 females who died at the age of 53.
If we assume that out of the 175 females, 30 females were of age 42 years in 2000, and they died in 2005, then 30 females died at the age of 47. Now, if we assume that there are 15 females of age 42 and 15 females of age 48 in the year 2000, and they all died in 2005, then we have 15 females who died at the age of 47 and 15 females who died at the age of 53.
So we can see that there are many cases possible. We are given that there were 250 females aged 20-30 in 1980, and in 2010, these females ages are from 50-60, but only 145 are alive in 2010.
In 2010 there were 145 females from age 50-60. If we assume that out of these, 40 females were of age 58 years in 2010 and they died in 2015, then there are 40 females who died at the age of 63.
If we assume that out of the 145 females, 40 females are of age 52 years age in 2010, and they died in 2015, then 40 females died at the age of 57. Now, if we assume that there are 15 females of age 52 and 25 females of age 58 in the year 2010, and they all died in 2015, then we have 15 females who died at the age of 57 and 25 females who died at the age of 63.
So we can see that again, there are many cases possible. In the first case, the range of values possible is from 0 to 30. In the
second case, the range of values possible is from 0 to 40. So in total, we get a range of possible values from 0 to 70.
Thus, only one possible value of this question is not possible.