CAT 2022 Slot 3 · DILR · Question 3
CAT 2022 Slot 3 previous year question on Reasoning Based DI, with the answer and a step-by-step solution.
Set 1: Mortality Study of 2000 Individuals — this question belongs to a set. Read the full set with all 5 questions →
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.
- A240
- B580
- C470
- D230
Answer & solution
Answer: Option C
Solving the set
Step 1 – Follow each 1980 age group (cohort) through the figures: a group aged 10–20 in 1980 is 20–30 in 1990, 30–40 in 2000, and so on. Each cohort starts with 250 males and 250 females.
Age in 1980 | Sex | 1980 | 1990 | 2000 | 2010 | 2020 |
10–20 | M | 250 | 230 (20–30) | 180 (30–40) | 150 (40–50) | 140 (50–60) |
10–20 | F | 250 | 240 | 210 | 160 | 100 |
20–30 | M | 250 | 235 (30–40) | 205 (40–50) | 165 (50–60) | 125 (60–70) |
20–30 | F | 250 | 225 | 175 | 145 | 105 |
30–40 | M | 250 | 210 (40–50) | 160 (50–60) | 90 (60–70) | 50 (70–80) |
30–40 | F | 250 | 190 | 150 | 100 | 60 |
40–50 | M | 250 | 190 (50–60) | 100 (60–70) | 25 (70–80) | 5 (80–90) |
40–50 | F | 250 | 220 | 120 | 30 | 18 |
Step 2 – Deaths in a decade for a cohort = number alive at the start of the decade − number alive at its end.
This question
The 10–20 and 20–30 cohorts of 1980 are aged 50–60 and 60–70 in 2020: (140 + 100) + (125 + 105) = 470.
Hence, the answer is option 3.
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