CAT 2022 Slot 3 · DILR · Set 1: Mortality Study of 2000 Individuals

The full set and all 5 questions (Q1–Q5) from CAT 2022 Slot 3, with answers and solutions.

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 · Reasoning Based DI

In 2000, what was the ratio of the number of dead males to dead females among those being tracked?

A
71 : 69
B
41 : 43
C
129 : 131
D
109 : 107

Pick an option, then check.

Answer & solution

Answer: Option A

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

From the cohort table, 2000: males alive 645, dead 1000 − 645 = 355; females alive 655, dead 345. 355 : 345 = 71 : 69.

Hence, the answer is option 1.

Question 2 · Reasoning Based DI

How many people who were being tracked and who were between 30 and 40 years of age in 1980 survived until 2010?

A
110
B
90
C
190
D
310

Pick an option, then check.

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 30–40 cohort of 1980 is aged 60–70 in 2010: 90 males + 100 females = 190 survived.

Hence, the answer is option 3.

Question 3 · Reasoning Based DI

How many individuals who were being tracked and who were less than 30 years of age in 1980 survived until 2020?

A
240
B
580
C
470
D
230

Pick an option, then check.

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.

Question 4 · Reasoning Based DI

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?

Answer & solution

Answer: 40

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 20–30 male cohort: 205 alive in 2000, 165 in 2010. Deaths in 2000–2010 = 40.

Hence, the answer is 40.

Question 5 · Reasoning Based DI

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?

Answer & solution

Answer: 30

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 20–30 female cohort: 175 alive in 2000 (aged 40–50) and 145 in 2010 (aged 50–60). The answer key takes the deaths in this decade, 175 − 145 = 30. (The figures give only decade snapshots, so this is the intended reading.)

Hence, the answer is 30.

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