CAT Data Interpretation Questions & Solutions

A sample of real CAT Data Interpretation past-year questions, each with a worked solution and the correct answer highlighted. AthenaPrep has 12 Data Interpretation questions in all — sign up free to practise them timed.

Passage
The Sustainability Index (SI) of a country at a point in time is an integer between 1 and 100. This question is related to SI of six countries - A, B, C, D, E, and F - at three different points in time - 2016, 2020, and 2024. The plot represents the exact changes in their SI, with X-coordinate representing % increase in 2020 from 2016, i.e., (SI in 2020 minus SI in 2016) / (SI in 2016), and Y-coordinate representing % increase in 2024 from 2020. At any point in time, the country with highest SI is ranked 1, while the country with the lowest SI is ranked 6. The following additional facts are known.
1. In 2016, B, C, E, and A had ranks 1, 2, 3, and 4 respectively.
2. F had lower SI than any other country in 2016, 2020, and 2024.
3. In 2024, E was the only country with SI of 90.
4. The range of SI of the six countries was 60 in 2016 as well as in 2024.
Q1.CAT 2025
What was the SI of E in 2016?
Answer: 60
Show solution
Let us assume the values of A, B, C, D, E and F to be a, b, c, d, e and f in 2016.

For A:

Value in 2020 = increased by 25% from 2016 = $\left(1\ +\ \dfrac{25}{100}\right)a$ = $\dfrac{5}{4}a$

Value in 2024 = increased by 50% from 2020 = $\left(1\ +\ \dfrac{50}{100}\right)\times\ \dfrac{5a}{4}$ = $\dfrac{15}{8}a$

For B:

Value in 2020 = decreased by 25% from 2016 = $\left(1\ -\ \dfrac{25}{100}\right)b$ = $\dfrac{3}{4}b$

Value in 2024 = decreased by 25% from 2020 = $\left(1\ -\ \dfrac{25}{100}\right)\times\ \dfrac{3b}{4}$ = $\dfrac{9}{16}b$

For C:

Value in 2020 = decreased by 20% from 2016 = $\left(1\ -\ \dfrac{20}{100}\right)c$ = $\dfrac{4}{5}c$

Value in 2024 = increased by 40% from 2020 = $\left(1\ +\ \dfrac{40}{100}\right)\times\ \dfrac{4c}{5}$ = $\dfrac{28}{25}c$

For D:

Value in 2020 = increased by 100% from 2016 = $\left(1\ +\ \dfrac{100}{100}\right)d$ = $2d$

Value in 2024 = increased by 20% from 2020 = $\left(1\ +\ \dfrac{20}{100}\right)\times\ 2d$ = $\dfrac{12}{5}d$

For E:

Value in 2020 = increased by 25% from 2016 = $\left(1\ +\ \dfrac{25}{100}\right)e$ = $\dfrac{5}{4}e$

Value in 2024 = increased by 20% from 2020 = $\left(1\ +\ \dfrac{20}{100}\right)\times\ \dfrac{5e}{4}$ = $\dfrac{3}{2}e$

For F:

Value in 2020 = increased by 100% from 2016 = $\left(1\ +\ \dfrac{100}{100}\right)f$ = $2f$

Value in 2024 = decreased by 25% from 2020 = $\left(1\ -\ \dfrac{25}{100}\right)\times\ 2f$ = $\dfrac{3}{2}f$

We are given that the value of E is 90 in 2024. We can calculate the value of e as,

$\dfrac{3e}{2}\ =\ 90$

$e\ =\ 60$

The value of E in 2016 is 60, and its value in 2020 can be calculated as,

$\dfrac{5e}{4}\ =\ \dfrac{5}{4}\times\ 60\ =\ 75$

We are given that B, C, E, and A had ranks 1, 2, 3, and 4, respectively, in 2016, and F has the lowest rank(6) in all the years.

Putting the values in the table, we get,

SI of E in 2016 is 60.

Hence, the correct answer is 60.
Q2.CAT 2025
What was the SI of F in 2020?
Answer: 40
Show solution
Let us assume the values of A, B, C, D, E and F to be a, b, c, d, e and f in 2016.

For A:

Value in 2020 = increased by 25% from 2016 = $\left(1\ +\ \dfrac{25}{100}\right)a$ = $\dfrac{5}{4}a$

Value in 2024 = increased by 50% from 2020 = $\left(1\ +\ \dfrac{50}{100}\right)\times\ \dfrac{5a}{4}$ = $\dfrac{15}{8}a$

For B:

Value in 2020 = decreased by 25% from 2016 = $\left(1\ -\ \dfrac{25}{100}\right)b$ = $\dfrac{3}{4}b$

Value in 2024 = decreased by 25% from 2020 = $\left(1\ -\ \dfrac{25}{100}\right)\times\ \dfrac{3b}{4}$ = $\dfrac{9}{16}b$

For C:

Value in 2020 = decreased by 20% from 2016 = $\left(1\ -\ \dfrac{20}{100}\right)c$ = $\dfrac{4}{5}c$

Value in 2024 = increased by 40% from 2020 = $\left(1\ +\ \dfrac{40}{100}\right)\times\ \dfrac{4c}{5}$ = $\dfrac{28}{25}c$

For D:

Value in 2020 = increased by 100% from 2016 = $\left(1\ +\ \dfrac{100}{100}\right)d$ = $2d$

Value in 2024 = increased by 20% from 2020 = $\left(1\ +\ \dfrac{20}{100}\right)\times\ 2d$ = $\dfrac{12}{5}d$

For E:

Value in 2020 = increased by 25% from 2016 = $\left(1\ +\ \dfrac{25}{100}\right)e$ = $\dfrac{5}{4}e$

Value in 2024 = increased by 20% from 2020 = $\left(1\ +\ \dfrac{20}{100}\right)\times\ \dfrac{5e}{4}$ = $\dfrac{3}{2}e$

For F:

Value in 2020 = increased by 100% from 2016 = $\left(1\ +\ \dfrac{100}{100}\right)f$ = $2f$

Value in 2024 = decreased by 25% from 2020 = $\left(1\ -\ \dfrac{25}{100}\right)\times\ 2f$ = $\dfrac{3}{2}f$

We are given that the value of E is 90 in 2024. We can calculate the value of e as,

$\dfrac{3e}{2}\ =\ 90$

$e\ =\ 60$

The value of E in 2016 is 60, and its value in 2020 can be calculated as,

$\dfrac{5e}{4}\ =\ \dfrac{5}{4}\times\ 60\ =\ 75$

We are given that B, C, E, and A had ranks 1, 2, 3, and 4, respectively, in 2016, and F has the lowest rank(6) in all the years.

Putting the values in the table, we get,

We know that F is ranked 6 and B is ranked 1 in 2016, and we are also given that the range of SI in 2016 and 2024 is 60. This means that the value of b-f = 60, and we can conclude that b is definitely greater than 60, as we know that f is an integer greater than 0.

We know that all the SI values in all the years are integers, and for SI of B to be an integer in 2024, the value of b must be a multiple of 16. The multiples of 16 that are greater than 60 and less than 100 are 64, 80 and 96.

CASE 1: b = 64

If b = 64, then the value of f becomes 4, as we know b - f = 60.

If f = 4, then the value of F in 2024 is 3f/2 = 12/2 = 6.

We already know the value of E in 2024 is 90.

In that case, the range of SI in 2024 is at least 90 - 6 = 84, but we are given that the range is 60 in 2024, which is not possible in this case.

So, we can eliminate this case.

CASE 2: b = 96

If b = 96, then the value of f becomes 36, as we know b - f = 60.

If f = 36, then the value of F in 2024 is 3f/2 = 108/2 = 54.

The value of B in 2024 = 9b/16 = (9 * 96)/16 = 54

We calculated the value of B and F to be 54 in 2024, which is not possible, as we are given that F had a lower SI than any other country in 2024, and we obtained its value to be the same as B.

So, we can eliminate this case.

CASE 3: b = 80

If b = 80, then the value of f becomes 20, as we know b - f = 60.

If f = 20, then the value of F in 2024 is 3f/2 = 60/2 = 30.

The value of B in 2024 = 9b/16 = (9 * 80)/16 = 45

We can see that no condition is violated in this case, as F is less than B in 2024, and the range in 2024 from the obtained values as of now is 90 - 30 = 60.

So, we can conclude that the value of b = 80 and f = 20.

Substituting the values in the table, we get,

So, SI of F in 2020 is 40.

Hence, the correct answer is 40.
Q3.CAT 2025
What was the SI of C in 2024?
Answer: 84
Show solution
Let us assume the values of A, B, C, D, E and F to be a, b, c, d, e and f in 2016.

For A:

Value in 2020 = increased by 25% from 2016 = $\left(1\ +\ \dfrac{25}{100}\right)a$ = $\dfrac{5}{4}a$

Value in 2024 = increased by 50% from 2020 = $\left(1\ +\ \dfrac{50}{100}\right)\times\ \dfrac{5a}{4}$ = $\dfrac{15}{8}a$

For B:

Value in 2020 = decreased by 25% from 2016 = $\left(1\ -\ \dfrac{25}{100}\right)b$ = $\dfrac{3}{4}b$

Value in 2024 = decreased by 25% from 2020 = $\left(1\ -\ \dfrac{25}{100}\right)\times\ \dfrac{3b}{4}$ = $\dfrac{9}{16}b$

For C:

Value in 2020 = decreased by 20% from 2016 = $\left(1\ -\ \dfrac{20}{100}\right)c$ = $\dfrac{4}{5}c$

Value in 2024 = increased by 40% from 2020 = $\left(1\ +\ \dfrac{40}{100}\right)\times\ \dfrac{4c}{5}$ = $\dfrac{28}{25}c$

For D:

Value in 2020 = increased by 100% from 2016 = $\left(1\ +\ \dfrac{100}{100}\right)d$ = $2d$

Value in 2024 = increased by 20% from 2020 = $\left(1\ +\ \dfrac{20}{100}\right)\times\ 2d$ = $\dfrac{12}{5}d$

For E:

Value in 2020 = increased by 25% from 2016 = $\left(1\ +\ \dfrac{25}{100}\right)e$ = $\dfrac{5}{4}e$

Value in 2024 = increased by 20% from 2020 = $\left(1\ +\ \dfrac{20}{100}\right)\times\ \dfrac{5e}{4}$ = $\dfrac{3}{2}e$

For F:

Value in 2020 = increased by 100% from 2016 = $\left(1\ +\ \dfrac{100}{100}\right)f$ = $2f$

Value in 2024 = decreased by 25% from 2020 = $\left(1\ -\ \dfrac{25}{100}\right)\times\ 2f$ = $\dfrac{3}{2}f$

We are given that the value of E is 90 in 2024. We can calculate the value of e as,

$\dfrac{3e}{2}\ =\ 90$

$e\ =\ 60$

The value of E in 2016 is 60, and its value in 2020 can be calculated as,

$\dfrac{5e}{4}\ =\ \dfrac{5}{4}\times\ 60\ =\ 75$

We are given that B, C, E, and A had ranks 1, 2, 3, and 4, respectively, in 2016, and F has the lowest rank(6) in all the years.

Putting the values in the table, we get,

We know that F is ranked 6 and B is ranked 1 in 2016, and we are also given that the range of SI in 2016 and 2024 is 60. This means that the value of b-f = 60, and we can conclude that b is definitely greater than 60, as we know that f is an integer greater than 0.

We know that all the SI values in all the years are integers, and for SI of B to be an integer in 2024, the value of b must be a multiple of 16. The multiples of 16 that are greater than 60 and less than 100 are 64, 80 and 96.

CASE 1: b = 64

If b = 64, then the value of f becomes 4, as we know b - f = 60.

If f = 4, then the value of F in 2024 is 3f/2 = 12/2 = 6.

We already know the value of E in 2024 is 90.

In that case, the range of SI in 2024 is at least 90 - 6 = 84, but we are given that the range is 60 in 2024, which is not possible in this case.

So, we can eliminate this case.

CASE 2: b = 96

If b = 96, then the value of f becomes 36, as we know b - f = 60.

If f = 36, then the value of F in 2024 is 3f/2 = 108/2 = 54.

The value of B in 2024 = 9b/16 = (9 * 96)/16 = 54

We calculated the value of B and F to be 54 in 2024, which is not possible, as we are given that F had a lower SI than any other country in 2024, and we obtained its value to be the same as B.

So, we can eliminate this case.

CASE 3: b = 80

If b = 80, then the value of f becomes 20, as we know b - f = 60.

If f = 20, then the value of F in 2024 is 3f/2 = 60/2 = 30.

The value of B in 2024 = 9b/16 = (9 * 80)/16 = 45

We can see that no condition is violated in this case, as F is less than B in 2024, and the range in 2024 from the obtained values as of now is 90 - 30 = 60.

So, we can conclude that the value of b = 80 and f = 20.

Substituting the values in the table, we get,

We know that C is ranked 2nd in 2016, and we know the values of 1st and 3rd to be 80 and 60. We also know that SI of C has to be integers in 2016, 2020 and 2024. So, for the value of SI of C to be an integer in 2024, the value of c has to be a multiple of 25.

So, we know that c lies between 80 and 60, and is also a multiple of 25. The only multiple of 25 that lies between 60 and 80 is 75. So, the value of c has to be 75, and the value of C in 2024 can be calculated as,

C in 2024 = 28c/25 = (28 * 75)/25 = 84.

Hence, the correct answer is 84.
Q4.CAT 2025
What was the SI of B in 2024?
- 60
- 54
- 80
- 45
Show solution
Let us assume the values of A, B, C, D, E and F to be a, b, c, d, e and f in 2016.

For A:

Value in 2020 = increased by 25% from 2016 = $\left(1\ +\ \dfrac{25}{100}\right)a$ = $\dfrac{5}{4}a$

Value in 2024 = increased by 50% from 2020 = $\left(1\ +\ \dfrac{50}{100}\right)\times\ \dfrac{5a}{4}$ = $\dfrac{15}{8}a$

For B:

Value in 2020 = decreased by 25% from 2016 = $\left(1\ -\ \dfrac{25}{100}\right)b$ = $\dfrac{3}{4}b$

Value in 2024 = decreased by 25% from 2020 = $\left(1\ -\ \dfrac{25}{100}\right)\times\ \dfrac{3b}{4}$ = $\dfrac{9}{16}b$

For C:

Value in 2020 = decreased by 20% from 2016 = $\left(1\ -\ \dfrac{20}{100}\right)c$ = $\dfrac{4}{5}c$

Value in 2024 = increased by 40% from 2020 = $\left(1\ +\ \dfrac{40}{100}\right)\times\ \dfrac{4c}{5}$ = $\dfrac{28}{25}c$

For D:

Value in 2020 = increased by 100% from 2016 = $\left(1\ +\ \dfrac{100}{100}\right)d$ = $2d$

Value in 2024 = increased by 20% from 2020 = $\left(1\ +\ \dfrac{20}{100}\right)\times\ 2d$ = $\dfrac{12}{5}d$

For E:

Value in 2020 = increased by 25% from 2016 = $\left(1\ +\ \dfrac{25}{100}\right)e$ = $\dfrac{5}{4}e$

Value in 2024 = increased by 20% from 2020 = $\left(1\ +\ \dfrac{20}{100}\right)\times\ \dfrac{5e}{4}$ = $\dfrac{3}{2}e$

For F:

Value in 2020 = increased by 100% from 2016 = $\left(1\ +\ \dfrac{100}{100}\right)f$ = $2f$

Value in 2024 = decreased by 25% from 2020 = $\left(1\ -\ \dfrac{25}{100}\right)\times\ 2f$ = $\dfrac{3}{2}f$

We are given that the value of E is 90 in 2024. We can calculate the value of e as,

$\dfrac{3e}{2}\ =\ 90$

$e\ =\ 60$

The value of E in 2016 is 60, and its value in 2020 can be calculated as,

$\dfrac{5e}{4}\ =\ \dfrac{5}{4}\times\ 60\ =\ 75$

We are given that B, C, E, and A had ranks 1, 2, 3, and 4, respectively, in 2016, and F has the lowest rank(6) in all the years.

Putting the values in the table, we get,

We know that F is ranked 6 and B is ranked 1 in 2016, and we are also given that the range of SI in 2016 and 2024 is 60. This means that the value of b-f = 60, and we can conclude that b is definitely greater than 60, as we know that f is an integer greater than 0.

We know that all the SI values in all the years are integers, and for SI of B to be an integer in 2024, the value of b must be a multiple of 16. The multiples of 16 that are greater than 60 and less than 100 are 64, 80 and 96.

CASE 1: b = 64

If b = 64, then the value of f becomes 4, as we know b - f = 60.

If f = 4, then the value of F in 2024 is 3f/2 = 12/2 = 6.

We already know the value of E in 2024 is 90.

In that case, the range of SI in 2024 is at least 90 - 6 = 84, but we are given that the range is 60 in 2024, which is not possible in this case.

So, we can eliminate this case.

CASE 2: b = 96

If b = 96, then the value of f becomes 36, as we know b - f = 60.

If f = 36, then the value of F in 2024 is 3f/2 = 108/2 = 54.

The value of B in 2024 = 9b/16 = (9 * 96)/16 = 54

We calculated the value of B and F to be 54 in 2024, which is not possible, as we are given that F had a lower SI than any other country in 2024, and we obtained its value to be the same as B.

So, we can eliminate this case.

CASE 3: b = 80

If b = 80, then the value of f becomes 20, as we know b - f = 60.

If f = 20, then the value of F in 2024 is 3f/2 = 60/2 = 30.

The value of B in 2024 = 9b/16 = (9 * 80)/16 = 45

We can see that no condition is violated in this case, as F is less than B in 2024, and the range in 2024 from the obtained values as of now is 90 - 30 = 60.

So, we can conclude that the value of b = 80 and f = 20.

Substituting the values in the table, we get,

So, SI of B in 2024 is 45.

Hence, the correct answer is option D.
Passage
The different bars in the diagram above provide information about different orders in various categories (Art, Binders, ….) that were booked in the first two weeks of September of a store for one client. The colour and pattern of a bar denotes the ship mode (First Class / Second Class / Standard Class). The left end point of a bar indicates the booking day of the order, while the right end point indicates the dispatch day of the order. The difference between the dispatch day and the booking day (measured in terms of the number of days) is called the processing time of the order. For the same category, an order is considered for booking only after the previous order of the same category is dispatched. No two consecutive orders of the same category had identical ship mode during this period.

For example, there were only two orders in the furnishing category during this period. The first one was shipped in the Second Class. It was booked on Sep 1 and dispatched on Sep 5. The second order was shipped in the Standard class. It was booked on Sep 5 (although the order might have been placed before that) and dispatched on Sep 12. So the processing times were 4 and 7 days respectively for these orders.
Q5.CAT 2021
How many days between Sep 1 and Sep 14 (both inclusive) had no booking from this client considering all the above categories?
Answer: 6
Show solution
Accumulating all the data :
We get the following table :

Note a-b : represents the duration where a is the day when order is booked and b is the day when it is dispatched .
Now No booking days from the table are : September 8,9,10,11,12 and 14.
So a total of 6 days .
Q6.CAT 2021
What was the average processing time of all orders in the categories which had only one type of ship mode?
Answer: 11
Show solution
Accumulating all the data :
We get the following table :

Note a-b : represents the duration where a is the day when order is booked and b is the day when it is dispatched .
Now Envelopes and Accessories has only 1 ship mode i.e Standard class .
So therefore processing days for envelopes = 7-3 =4
and processing days for accessories = 19-1 =18
Therefore average = $\frac{\left(18+4\right)}{2}=11$
Q7.CAT 2021
The sequence of categories -- Art, Binders, Paper and Phones -- in decreasing order of average processing time of their orders in this period is:
- Art, Binders, Paper, Phones
- Phones, Art, Binders, Paper
- Phones, Binders, Art, Paper
- Paper, Binders, Art, Phones
Show solution
Accumulating all the data :
We get the following table :

Note a-b : represents the duration where a is the day when order is booked and b is the day when it is dispatched .

Now taking average processing time per order for the above mentioned categories we get :
Art = $\frac{2+8+2+1+7}{5}\ \ =4$
Binders = $\frac{1+1+11+2}{4}\ \ =3.75$
Papers = $\frac{3+2+5}{3}\ \ =3.33$
Phones = $\frac{2+12+1}{3}\ \ =5$
So in decreasing order we get Phones , Art ,Binder , Paper.
Q8.CAT 2021
Approximately what percentage of orders had a processing time of one day during the period Sep 1 to Sep 22 (both dates inclusive)?
- 22%
- 16%
- 20%
- 25%
Show solution
Accumulating all the data :
We get the following table :

Note a-b : represents the duration where a is the day when order is booked and b is the day when it is dispatched .

Now from the table we observe that the total number of orders are 35 and 7 orders have a processing time of 1 unit
The 7 orders are : Arts Standard class,Binders First class and standard class, Phones First class, Bookcases second class ( 2 orders) and Chairs standard class.
So the percentage = $\frac{7}{35}\times\ 100\ =\ 20$
Passage
The figure above shows the schedule of four employees - Abani, Bahni, Danni, and Tinni - whom Dhoni supervised in 2020. Altogether there were five projects which started and concluded in 2020 in which they were involved. For each of these projects and for each employee, the starting day was at the beginning of a month and the concluding day was the end of a month, and these are indicated by the left and right end points of the corresponding horizontal bars. The number within each bar indicates the percentage of assigned work completed by the employee for that project, as assessed by Dhoni.

For each employee, his/her total project-month (in 2020) is the sum of the number of months (s)he worked across the five projects, while his/her annual completion index is the weightage average of the completion percentage assigned from the different projects, with the weights being the corresponding number of months (s)he worked in these projects. For each project, the total employee-month is the sum of the number of months four employees worked in this project, while its completion index is the weightage average of the completion percentage assigned for the employees who worked in this project, with the weights being the corresponding number of months they worked in this project.
Q9.CAT 2021
Which of the following statements is/are true?

I: The total project-month was the same for the four employees.
II: The total employee-month was the same for the five projects.
- Only II
- Both I and II
- Neither I nor II
- Only I
Show solution
The total project month is the number of months Abani, Bahni, Danni, and Tinni individually worked for all the projects combined :

Abani - 2+2+5 = 9 months

Bahni - 2+4+3 = 9 months

Danni - 3+3+2+1 = 9 months

Tinni - 2+2+3+2 = 9 months.

The total employee month for all the five projects is the sum of the total employee-month is the sum of the number of months four employees worked in this project.

Project -1 = 2+2+2 = 6 months

Project -2 = 3+2 = 5 months

Project - 3 = 2+4+3 = 9 months.

Project - 4 = 5+2+3 = 10 months.

Project - 5 = 3+1+2 = 6 months.

Only statement 1 is true.
Q10.CAT 2021
Which employees did not work in multiple projects for any of the months in 2020?
- Only Abani, Bahni and Danni
- Only Abani and Bahni
- All four of them
- Only Tinni
Show solution
Abani, Banni, and Danni did not work on multiple projects simultaneously in a month

Tinni was the only person who worked on multiple projects which are project 4 and project 5 in the month of september.
Q11.CAT 2021
The project duration, measured in terms of the number of months, is the time during which at least one employee worked in the project. Which of the following pairs of the projects had the same duration?
- Project 1, Project 5
- Project 4, Project 5
- Project 3, Project 5
- Project 3, Project 4
Show solution
Considering the information provided :

For project 1 : 3 months.

Project - 2: 3 months.

Project - 3: 5 months.

Project - 4: 5 months.

Project - 5: 4 months.

Among the given options option D is true which is project 3, project 4.
Q12.CAT 2021
The list of employees in decreasing order of annual completion index is:
- Danni, Tinni, Bahni, Abani
- Bahni, Abani, Tinni, Danni
- Danni, Tinni, Abani, Bahni
- Tinni, Danni, Abani, Bahni
Show solution
The annual completion index for different people is :

The weightage average of the completion percentage assigned from the different projects, with the weights being the corresponding number of months (s)he worked in these projects.

For Abani :

$\frac{\left(\left(100\cdot2\right)+\left(100\cdot2\right)+\left(80\cdot5\right)\right)}{2+2+5}=\ \frac{800}{9}$

For Bahni :

$\frac{\left(\left(100\cdot2\right)+\left(75\cdot4\right)+\left(90\cdot3\right)\right)}{2+3+4}=\ \frac{770}{9}$

For Danni :

$\frac{\left(\left(90\cdot3\right)+\left(100\cdot3\right)+\left(100\cdot2\right)+\left(100\cdot1\right)\right)}{2+3+2+1}=\ \frac{870}{9}$

For Tinni :

$\frac{\left(\left(80\cdot2\right)+\left(100\cdot2\right)+\left(100\cdot3\right)+\left(100\cdot2\right)\right)}{2+2+3+2}=\ \frac{860}{9}$

The descending order for the four people is :

Danni, Tinni, Abani, Bahni.

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CAT Data Interpretation Questions & Solutions

Passage

The Sustainability Index (SI) of a country at a point in time is an integer between 1 and 100. This question is related to SI of six countries - A, B, C, D, E, and F - at three different points in time - 2016, 2020, and 2024. The plot represents the exact changes in their SI, with X-coordinate representing % increase in 2020 from 2016, i.e., (SI in 2020 minus SI in 2016) / (SI in 2016), and Y-coordinate representing % increase in 2024 from 2020. At any point in time, the country with highest SI is ranked 1, while the country with the lowest SI is ranked 6. The following additional facts are known.
1. In 2016, B, C, E, and A had ranks 1, 2, 3, and 4 respectively.
2. F had lower SI than any other country in 2016, 2020, and 2024.
3. In 2024, E was the only country with SI of 90.
4. The range of SI of the six countries was 60 in 2016 as well as in 2024.

Q1.CAT 2025

What was the SI of E in 2016?

Answer: 60

Show solution

Let us assume the values of A, B, C, D, E and F to be a, b, c, d, e and f in 2016.

For A:

Value in 2020 = increased by 25% from 2016 = $\left(1\ +\ \dfrac{25}{100}\right)a$ = $\dfrac{5}{4}a$

Value in 2024 = increased by 50% from 2020 = $\left(1\ +\ \dfrac{50}{100}\right)\times\ \dfrac{5a}{4}$ = $\dfrac{15}{8}a$

For B:

Value in 2020 = decreased by 25% from 2016 = $\left(1\ -\ \dfrac{25}{100}\right)b$ = $\dfrac{3}{4}b$

Value in 2024 = decreased by 25% from 2020 = $\left(1\ -\ \dfrac{25}{100}\right)\times\ \dfrac{3b}{4}$ = $\dfrac{9}{16}b$

For C:

Value in 2020 = decreased by 20% from 2016 = $\left(1\ -\ \dfrac{20}{100}\right)c$ = $\dfrac{4}{5}c$

Value in 2024 = increased by 40% from 2020 = $\left(1\ +\ \dfrac{40}{100}\right)\times\ \dfrac{4c}{5}$ = $\dfrac{28}{25}c$

For D:

Value in 2020 = increased by 100% from 2016 = $\left(1\ +\ \dfrac{100}{100}\right)d$ = $2d$

Value in 2024 = increased by 20% from 2020 = $\left(1\ +\ \dfrac{20}{100}\right)\times\ 2d$ = $\dfrac{12}{5}d$

For E:

Value in 2020 = increased by 25% from 2016 = $\left(1\ +\ \dfrac{25}{100}\right)e$ = $\dfrac{5}{4}e$

Value in 2024 = increased by 20% from 2020 = $\left(1\ +\ \dfrac{20}{100}\right)\times\ \dfrac{5e}{4}$ = $\dfrac{3}{2}e$

For F:

Value in 2020 = increased by 100% from 2016 = $\left(1\ +\ \dfrac{100}{100}\right)f$ = $2f$

Value in 2024 = decreased by 25% from 2020 = $\left(1\ -\ \dfrac{25}{100}\right)\times\ 2f$ = $\dfrac{3}{2}f$

We are given that the value of E is 90 in 2024. We can calculate the value of e as,

$\dfrac{3e}{2}\ =\ 90$

$e\ =\ 60$

The value of E in 2016 is 60, and its value in 2020 can be calculated as,

$\dfrac{5e}{4}\ =\ \dfrac{5}{4}\times\ 60\ =\ 75$

We are given that B, C, E, and A had ranks 1, 2, 3, and 4, respectively, in 2016, and F has the lowest rank(6) in all the years.

Putting the values in the table, we get,

SI of E in 2016 is 60.

Hence, the correct answer is 60.

Q2.CAT 2025

What was the SI of F in 2020?

Answer: 40

Show solution

Let us assume the values of A, B, C, D, E and F to be a, b, c, d, e and f in 2016.

For A:

Value in 2020 = increased by 25% from 2016 = $\left(1\ +\ \dfrac{25}{100}\right)a$ = $\dfrac{5}{4}a$

Value in 2024 = increased by 50% from 2020 = $\left(1\ +\ \dfrac{50}{100}\right)\times\ \dfrac{5a}{4}$ = $\dfrac{15}{8}a$

For B:

Value in 2020 = decreased by 25% from 2016 = $\left(1\ -\ \dfrac{25}{100}\right)b$ = $\dfrac{3}{4}b$

Value in 2024 = decreased by 25% from 2020 = $\left(1\ -\ \dfrac{25}{100}\right)\times\ \dfrac{3b}{4}$ = $\dfrac{9}{16}b$

For C:

Value in 2020 = decreased by 20% from 2016 = $\left(1\ -\ \dfrac{20}{100}\right)c$ = $\dfrac{4}{5}c$

Value in 2024 = increased by 40% from 2020 = $\left(1\ +\ \dfrac{40}{100}\right)\times\ \dfrac{4c}{5}$ = $\dfrac{28}{25}c$

For D:

Value in 2020 = increased by 100% from 2016 = $\left(1\ +\ \dfrac{100}{100}\right)d$ = $2d$

Value in 2024 = increased by 20% from 2020 = $\left(1\ +\ \dfrac{20}{100}\right)\times\ 2d$ = $\dfrac{12}{5}d$

For E:

Value in 2020 = increased by 25% from 2016 = $\left(1\ +\ \dfrac{25}{100}\right)e$ = $\dfrac{5}{4}e$

Value in 2024 = increased by 20% from 2020 = $\left(1\ +\ \dfrac{20}{100}\right)\times\ \dfrac{5e}{4}$ = $\dfrac{3}{2}e$

For F:

Value in 2020 = increased by 100% from 2016 = $\left(1\ +\ \dfrac{100}{100}\right)f$ = $2f$

Value in 2024 = decreased by 25% from 2020 = $\left(1\ -\ \dfrac{25}{100}\right)\times\ 2f$ = $\dfrac{3}{2}f$

We are given that the value of E is 90 in 2024. We can calculate the value of e as,

$\dfrac{3e}{2}\ =\ 90$

$e\ =\ 60$

The value of E in 2016 is 60, and its value in 2020 can be calculated as,

$\dfrac{5e}{4}\ =\ \dfrac{5}{4}\times\ 60\ =\ 75$

We are given that B, C, E, and A had ranks 1, 2, 3, and 4, respectively, in 2016, and F has the lowest rank(6) in all the years.

Putting the values in the table, we get,

We know that F is ranked 6 and B is ranked 1 in 2016, and we are also given that the range of SI in 2016 and 2024 is 60. This means that the value of b-f = 60, and we can conclude that b is definitely greater than 60, as we know that f is an integer greater than 0.

We know that all the SI values in all the years are integers, and for SI of B to be an integer in 2024, the value of b must be a multiple of 16. The multiples of 16 that are greater than 60 and less than 100 are 64, 80 and 96.

CASE 1: b = 64

If b = 64, then the value of f becomes 4, as we know b - f = 60.

If f = 4, then the value of F in 2024 is 3f/2 = 12/2 = 6.

We already know the value of E in 2024 is 90.

In that case, the range of SI in 2024 is at least 90 - 6 = 84, but we are given that the range is 60 in 2024, which is not possible in this case.

So, we can eliminate this case.

CASE 2: b = 96

If b = 96, then the value of f becomes 36, as we know b - f = 60.

If f = 36, then the value of F in 2024 is 3f/2 = 108/2 = 54.

The value of B in 2024 = 9b/16 = (9 * 96)/16 = 54

We calculated the value of B and F to be 54 in 2024, which is not possible, as we are given that F had a lower SI than any other country in 2024, and we obtained its value to be the same as B.

So, we can eliminate this case.

CASE 3: b = 80

If b = 80, then the value of f becomes 20, as we know b - f = 60.

If f = 20, then the value of F in 2024 is 3f/2 = 60/2 = 30.

The value of B in 2024 = 9b/16 = (9 * 80)/16 = 45

We can see that no condition is violated in this case, as F is less than B in 2024, and the range in 2024 from the obtained values as of now is 90 - 30 = 60.

So, we can conclude that the value of b = 80 and f = 20.

Substituting the values in the table, we get,

So, SI of F in 2020 is 40.

Hence, the correct answer is 40.

Q3.CAT 2025

What was the SI of C in 2024?

Answer: 84

Show solution

Let us assume the values of A, B, C, D, E and F to be a, b, c, d, e and f in 2016.

For A:

Value in 2020 = increased by 25% from 2016 = $\left(1\ +\ \dfrac{25}{100}\right)a$ = $\dfrac{5}{4}a$

Value in 2024 = increased by 50% from 2020 = $\left(1\ +\ \dfrac{50}{100}\right)\times\ \dfrac{5a}{4}$ = $\dfrac{15}{8}a$

For B:

Value in 2020 = decreased by 25% from 2016 = $\left(1\ -\ \dfrac{25}{100}\right)b$ = $\dfrac{3}{4}b$

Value in 2024 = decreased by 25% from 2020 = $\left(1\ -\ \dfrac{25}{100}\right)\times\ \dfrac{3b}{4}$ = $\dfrac{9}{16}b$

For C:

Value in 2020 = decreased by 20% from 2016 = $\left(1\ -\ \dfrac{20}{100}\right)c$ = $\dfrac{4}{5}c$

Value in 2024 = increased by 40% from 2020 = $\left(1\ +\ \dfrac{40}{100}\right)\times\ \dfrac{4c}{5}$ = $\dfrac{28}{25}c$

For D:

Value in 2020 = increased by 100% from 2016 = $\left(1\ +\ \dfrac{100}{100}\right)d$ = $2d$

Value in 2024 = increased by 20% from 2020 = $\left(1\ +\ \dfrac{20}{100}\right)\times\ 2d$ = $\dfrac{12}{5}d$

For E:

Value in 2020 = increased by 25% from 2016 = $\left(1\ +\ \dfrac{25}{100}\right)e$ = $\dfrac{5}{4}e$

Value in 2024 = increased by 20% from 2020 = $\left(1\ +\ \dfrac{20}{100}\right)\times\ \dfrac{5e}{4}$ = $\dfrac{3}{2}e$

For F:

Value in 2020 = increased by 100% from 2016 = $\left(1\ +\ \dfrac{100}{100}\right)f$ = $2f$

Value in 2024 = decreased by 25% from 2020 = $\left(1\ -\ \dfrac{25}{100}\right)\times\ 2f$ = $\dfrac{3}{2}f$

We are given that the value of E is 90 in 2024. We can calculate the value of e as,

$\dfrac{3e}{2}\ =\ 90$

$e\ =\ 60$

The value of E in 2016 is 60, and its value in 2020 can be calculated as,

$\dfrac{5e}{4}\ =\ \dfrac{5}{4}\times\ 60\ =\ 75$

We are given that B, C, E, and A had ranks 1, 2, 3, and 4, respectively, in 2016, and F has the lowest rank(6) in all the years.

Putting the values in the table, we get,

CASE 1: b = 64

If b = 64, then the value of f becomes 4, as we know b - f = 60.

If f = 4, then the value of F in 2024 is 3f/2 = 12/2 = 6.

We already know the value of E in 2024 is 90.

In that case, the range of SI in 2024 is at least 90 - 6 = 84, but we are given that the range is 60 in 2024, which is not possible in this case.

So, we can eliminate this case.

CASE 2: b = 96

If b = 96, then the value of f becomes 36, as we know b - f = 60.

If f = 36, then the value of F in 2024 is 3f/2 = 108/2 = 54.

The value of B in 2024 = 9b/16 = (9 * 96)/16 = 54

We calculated the value of B and F to be 54 in 2024, which is not possible, as we are given that F had a lower SI than any other country in 2024, and we obtained its value to be the same as B.

So, we can eliminate this case.

CASE 3: b = 80

If b = 80, then the value of f becomes 20, as we know b - f = 60.

If f = 20, then the value of F in 2024 is 3f/2 = 60/2 = 30.

The value of B in 2024 = 9b/16 = (9 * 80)/16 = 45

We can see that no condition is violated in this case, as F is less than B in 2024, and the range in 2024 from the obtained values as of now is 90 - 30 = 60.

So, we can conclude that the value of b = 80 and f = 20.

Substituting the values in the table, we get,

We know that C is ranked 2nd in 2016, and we know the values of 1st and 3rd to be 80 and 60. We also know that SI of C has to be integers in 2016, 2020 and 2024. So, for the value of SI of C to be an integer in 2024, the value of c has to be a multiple of 25.

So, we know that c lies between 80 and 60, and is also a multiple of 25. The only multiple of 25 that lies between 60 and 80 is 75. So, the value of c has to be 75, and the value of C in 2024 can be calculated as,

C in 2024 = 28c/25 = (28 * 75)/25 = 84.

Hence, the correct answer is 84.

Q4.CAT 2025

What was the SI of B in 2024?

Show solution

Let us assume the values of A, B, C, D, E and F to be a, b, c, d, e and f in 2016.

For A:

Value in 2020 = increased by 25% from 2016 = $\left(1\ +\ \dfrac{25}{100}\right)a$ = $\dfrac{5}{4}a$

Value in 2024 = increased by 50% from 2020 = $\left(1\ +\ \dfrac{50}{100}\right)\times\ \dfrac{5a}{4}$ = $\dfrac{15}{8}a$

For B:

Value in 2020 = decreased by 25% from 2016 = $\left(1\ -\ \dfrac{25}{100}\right)b$ = $\dfrac{3}{4}b$

Value in 2024 = decreased by 25% from 2020 = $\left(1\ -\ \dfrac{25}{100}\right)\times\ \dfrac{3b}{4}$ = $\dfrac{9}{16}b$

For C:

Value in 2020 = decreased by 20% from 2016 = $\left(1\ -\ \dfrac{20}{100}\right)c$ = $\dfrac{4}{5}c$

Value in 2024 = increased by 40% from 2020 = $\left(1\ +\ \dfrac{40}{100}\right)\times\ \dfrac{4c}{5}$ = $\dfrac{28}{25}c$

For D:

Value in 2020 = increased by 100% from 2016 = $\left(1\ +\ \dfrac{100}{100}\right)d$ = $2d$

Value in 2024 = increased by 20% from 2020 = $\left(1\ +\ \dfrac{20}{100}\right)\times\ 2d$ = $\dfrac{12}{5}d$

For E:

Value in 2020 = increased by 25% from 2016 = $\left(1\ +\ \dfrac{25}{100}\right)e$ = $\dfrac{5}{4}e$

Value in 2024 = increased by 20% from 2020 = $\left(1\ +\ \dfrac{20}{100}\right)\times\ \dfrac{5e}{4}$ = $\dfrac{3}{2}e$

For F:

Value in 2020 = increased by 100% from 2016 = $\left(1\ +\ \dfrac{100}{100}\right)f$ = $2f$

Value in 2024 = decreased by 25% from 2020 = $\left(1\ -\ \dfrac{25}{100}\right)\times\ 2f$ = $\dfrac{3}{2}f$

We are given that the value of E is 90 in 2024. We can calculate the value of e as,

$\dfrac{3e}{2}\ =\ 90$

$e\ =\ 60$

The value of E in 2016 is 60, and its value in 2020 can be calculated as,

$\dfrac{5e}{4}\ =\ \dfrac{5}{4}\times\ 60\ =\ 75$

We are given that B, C, E, and A had ranks 1, 2, 3, and 4, respectively, in 2016, and F has the lowest rank(6) in all the years.

Putting the values in the table, we get,

CASE 1: b = 64

If b = 64, then the value of f becomes 4, as we know b - f = 60.

If f = 4, then the value of F in 2024 is 3f/2 = 12/2 = 6.

We already know the value of E in 2024 is 90.

In that case, the range of SI in 2024 is at least 90 - 6 = 84, but we are given that the range is 60 in 2024, which is not possible in this case.

So, we can eliminate this case.

CASE 2: b = 96

If b = 96, then the value of f becomes 36, as we know b - f = 60.

If f = 36, then the value of F in 2024 is 3f/2 = 108/2 = 54.

The value of B in 2024 = 9b/16 = (9 * 96)/16 = 54

We calculated the value of B and F to be 54 in 2024, which is not possible, as we are given that F had a lower SI than any other country in 2024, and we obtained its value to be the same as B.

So, we can eliminate this case.

CASE 3: b = 80

If b = 80, then the value of f becomes 20, as we know b - f = 60.

If f = 20, then the value of F in 2024 is 3f/2 = 60/2 = 30.

The value of B in 2024 = 9b/16 = (9 * 80)/16 = 45

We can see that no condition is violated in this case, as F is less than B in 2024, and the range in 2024 from the obtained values as of now is 90 - 30 = 60.

So, we can conclude that the value of b = 80 and f = 20.

Substituting the values in the table, we get,

So, SI of B in 2024 is 45.

Hence, the correct answer is option D.

Passage

The different bars in the diagram above provide information about different orders in various categories (Art, Binders, ….) that were booked in the first two weeks of September of a store for one client. The colour and pattern of a bar denotes the ship mode (First Class / Second Class / Standard Class). The left end point of a bar indicates the booking day of the order, while the right end point indicates the dispatch day of the order. The difference between the dispatch day and the booking day (measured in terms of the number of days) is called the processing time of the order. For the same category, an order is considered for booking only after the previous order of the same category is dispatched. No two consecutive orders of the same category had identical ship mode during this period.

For example, there were only two orders in the furnishing category during this period. The first one was shipped in the Second Class. It was booked on Sep 1 and dispatched on Sep 5. The second order was shipped in the Standard class. It was booked on Sep 5 (although the order might have been placed before that) and dispatched on Sep 12. So the processing times were 4 and 7 days respectively for these orders.

Q5.CAT 2021

How many days between Sep 1 and Sep 14 (both inclusive) had no booking from this client considering all the above categories?

Answer: 6

Show solution

Accumulating all the data :
We get the following table :

Note a-b : represents the duration where a is the day when order is booked and b is the day when it is dispatched .
Now No booking days from the table are : September 8,9,10,11,12 and 14.
So a total of 6 days .

Q6.CAT 2021

What was the average processing time of all orders in the categories which had only one type of ship mode?

Answer: 11

Show solution

Accumulating all the data :
We get the following table :

Note a-b : represents the duration where a is the day when order is booked and b is the day when it is dispatched .
Now Envelopes and Accessories has only 1 ship mode i.e Standard class .
So therefore processing days for envelopes = 7-3 =4
and processing days for accessories = 19-1 =18
Therefore average = $\frac{\left(18+4\right)}{2}=11$

Q7.CAT 2021

The sequence of categories -- Art, Binders, Paper and Phones -- in decreasing order of average processing time of their orders in this period is:

Art, Binders, Paper, Phones
Phones, Art, Binders, Paper
Phones, Binders, Art, Paper
Paper, Binders, Art, Phones

Show solution

Accumulating all the data :
We get the following table :

Note a-b : represents the duration where a is the day when order is booked and b is the day when it is dispatched .

Now taking average processing time per order for the above mentioned categories we get :
Art = $\frac{2+8+2+1+7}{5}\ \ =4$
Binders = $\frac{1+1+11+2}{4}\ \ =3.75$
Papers = $\frac{3+2+5}{3}\ \ =3.33$
Phones = $\frac{2+12+1}{3}\ \ =5$
So in decreasing order we get Phones , Art ,Binder , Paper.

Q8.CAT 2021

Approximately what percentage of orders had a processing time of one day during the period Sep 1 to Sep 22 (both dates inclusive)?

Show solution

Accumulating all the data :
We get the following table :

Note a-b : represents the duration where a is the day when order is booked and b is the day when it is dispatched .

Now from the table we observe that the total number of orders are 35 and 7 orders have a processing time of 1 unit
The 7 orders are : Arts Standard class,Binders First class and standard class, Phones First class, Bookcases second class ( 2 orders) and Chairs standard class.
So the percentage = $\frac{7}{35}\times\ 100\ =\ 20$

Passage

The figure above shows the schedule of four employees - Abani, Bahni, Danni, and Tinni - whom Dhoni supervised in 2020. Altogether there were five projects which started and concluded in 2020 in which they were involved. For each of these projects and for each employee, the starting day was at the beginning of a month and the concluding day was the end of a month, and these are indicated by the left and right end points of the corresponding horizontal bars. The number within each bar indicates the percentage of assigned work completed by the employee for that project, as assessed by Dhoni.

For each employee, his/her total project-month (in 2020) is the sum of the number of months (s)he worked across the five projects, while his/her annual completion index is the weightage average of the completion percentage assigned from the different projects, with the weights being the corresponding number of months (s)he worked in these projects. For each project, the total employee-month is the sum of the number of months four employees worked in this project, while its completion index is the weightage average of the completion percentage assigned for the employees who worked in this project, with the weights being the corresponding number of months they worked in this project.

Q9.CAT 2021

Which of the following statements is/are true?

I: The total project-month was the same for the four employees.
II: The total employee-month was the same for the five projects.

Only II
Both I and II
Neither I nor II
Only I

Show solution

The total project month is the number of months Abani, Bahni, Danni, and Tinni individually worked for all the projects combined :

Abani - 2+2+5 = 9 months

Bahni - 2+4+3 = 9 months

Danni - 3+3+2+1 = 9 months

Tinni - 2+2+3+2 = 9 months.

The total employee month for all the five projects is the sum of the total employee-month is the sum of the number of months four employees worked in this project.

Project -1 = 2+2+2 = 6 months

Project -2 = 3+2 = 5 months

Project - 3 = 2+4+3 = 9 months.

Project - 4 = 5+2+3 = 10 months.

Project - 5 = 3+1+2 = 6 months.

Only statement 1 is true.

Q10.CAT 2021

Which employees did not work in multiple projects for any of the months in 2020?

Only Abani, Bahni and Danni
Only Abani and Bahni
All four of them
Only Tinni

Show solution

Abani, Banni, and Danni did not work on multiple projects simultaneously in a month

Tinni was the only person who worked on multiple projects which are project 4 and project 5 in the month of september.

Q11.CAT 2021

The project duration, measured in terms of the number of months, is the time during which at least one employee worked in the project. Which of the following pairs of the projects had the same duration?

Project 1, Project 5
Project 4, Project 5
Project 3, Project 5
Project 3, Project 4

Show solution

Considering the information provided :

For project 1 : 3 months.

Project - 2: 3 months.

Project - 3: 5 months.

Project - 4: 5 months.

Project - 5: 4 months.

Among the given options option D is true which is project 3, project 4.

Q12.CAT 2021

The list of employees in decreasing order of annual completion index is:

Danni, Tinni, Bahni, Abani
Bahni, Abani, Tinni, Danni
Danni, Tinni, Abani, Bahni
Tinni, Danni, Abani, Bahni

Show solution

The annual completion index for different people is :

The weightage average of the completion percentage assigned from the different projects, with the weights being the corresponding number of months (s)he worked in these projects.

For Abani :

$\frac{\left(\left(100\cdot2\right)+\left(100\cdot2\right)+\left(80\cdot5\right)\right)}{2+2+5}=\ \frac{800}{9}$

For Bahni :

$\frac{\left(\left(100\cdot2\right)+\left(75\cdot4\right)+\left(90\cdot3\right)\right)}{2+3+4}=\ \frac{770}{9}$

For Danni :

$\frac{\left(\left(90\cdot3\right)+\left(100\cdot3\right)+\left(100\cdot2\right)+\left(100\cdot1\right)\right)}{2+3+2+1}=\ \frac{870}{9}$

For Tinni :

$\frac{\left(\left(80\cdot2\right)+\left(100\cdot2\right)+\left(100\cdot3\right)+\left(100\cdot2\right)\right)}{2+2+3+2}=\ \frac{860}{9}$

The descending order for the four people is :

Danni, Tinni, Abani, Bahni.

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