CAT DI Charts Questions & Solutions

A sample of real CAT DI Charts past-year questions, each with a worked solution and the correct answer highlighted. AthenaPrep has 163 DI Charts questions in all — sign up free to practise them timed.

Passage
The chart below provides complete information about the number of countries visited by Dheeraj, Samantha and Nitesh, in Asia, Europe and the rest of the world (ROW).

The following additional facts are known about the countries visited by them.
1. 32 countries were visited by at least one of them.
2. USA (in ROW) is the only country that was visited by all three of them.
3. China (in Asia) is the only country that was visited by both Dheeraj and Nitesh, but not by Samantha.
4. France (in Europe) is the only country outside Asia, which was visited by both Dheeraj and Samantha, but not by Nitesh.
5. Half of the countries visited by both Samantha and Nitesh are in Europe.
Q1.CAT 2024
How many countries in Asia were visited by at least one of Dheeraj, Samantha and Nitesh?
Answer: 3
Show solution
Writing down the data with us in a table form.

But this includes countries which have been visited by one person, two people and three people. Essentially, there is an overlap of countries.
It is given to us that 32 distinct countries were visited among the three people,
Using that we can write down the equations,
$I+II+III=32$ ...(1)
$I+2II+3III=43$ ...(2)
Where I, II, and III denote the number of countries visited exactly by 1 of them, 2 of them and all of them.
We are told that USA(ROW) is the only country which was visited by all three people, that means $III=1$

Subtracting Equation 1 from 2 we get, $II+2III=11$
And since III=1 we get $II=9$

So, we are looking for 9 countries visited by exactly 2 people, and 22 countries visited by exactly 1 person.
Using the information from the problem set, we can note down the following,

We can see that Dheeraj visited only 1 country in ROW so every other value in that column has to be zero for wherever Dinesh is present. And Samantha has not visited any country in Asia so every value with Samantha present in Asia should be zero as well.

We have the following distribution, we are looking for 9 countries visited by exactly 2 people. And we have identified 2 countries, that means, 7 were countries were visited by both Samantha and Nitesh only. And given that half the countries visited by both of them are in Europe, and total number of countries visited by both of them is 7(only two of them)+1(USA)=8, they visited 4 countries in Europe together and 3 countries in ROW together. And using that information, we can fill in the rest of the table as well. Since we know the number of countries visited by each of them in a particular continent.

How many countries in Asia were visited by at least one of Dheeraj, Samantha and Nitesh is 3.
Passage
Comprehension:
Over the top (OTT) subscribers of a platform are segregated into three categories: i) Kid, ii)Elder, and iii) Others. Some of the subscribers used one app and the others used multiple apps to access the platform. The figure below shows the percentage of the total number of subscribers in 2023 and 2024 who belong to the ‘Kid’ and ‘Elder’ categories.

The following additional facts are known about the numbers of subscribers.
1. The total number of subscribers increased by 10% from 2023 to 2024.
2. In 2024, 1/2 of the subscribers from the ‘Kid’ category and 2/3 of the subscribers from the ‘Elder’ category subscribers use one app.
3. In 2023, the number of subscribers from the ‘Kid’ category who used multiple apps was the same as the number of subscribers from the ‘Elder’ category who used one app.
4. 10,000 subscribers from the ‘Kid’ category used one app and 15,000 subscribers from the ‘Elder’ category used multiple apps in 2023.
Q2.CAT 2024
How many subscribers belonged to the ‘Others’ category in 2024?
- Cannot be determined
- 65000
- 55000
- 45000
Show solution
Reading the bar graphs, we can find the distribution of the subscribers as:

Taking clue one into consideration, let's take the total number of subscribers in 2023 as 100x and in 2204 as 110x
This would give the split of subscribers as follows:

Clue 2 says that half of 22x, which is 11x and 2/3 of 33x, which is 22x, used one app, given that in 2024, out of 55x, 33x used one app.

Clues 3 and 4 are to be used with each other.
Clue 4 says that out of 15x kids, 10,000 used one app, and out of 20x Elders, 15,000 used multiple apps.
Clue 3 says that the kids who used multiple apps (15x - 10000) were the same as Elders who used one app (20x - 15000)

Equating these two we get:
15x- 10000 = 20x - 15000
5x = 5000
x = 1000

The first question asks about the number of others in 2024, which is 55x, or simply 55,000

Therefore, Option C is the correct answer.
Passage
The Ministry of Home Affairs is analysing crimes committed by foreigners in different states and union territories (UT) of India. All cases refer to the ones registered against foreigners in 2016.

The number of cases - classified into three categories: IPC crimes, SLL crimes and other crimes - for nine states/UTs are shown in the figure below. These nine belong to the top ten states/UTs in terms of the total number of cases registered. The remaining state (among top ten) is West Bengal, where all the 520 cases registered were SLL crimes.

The table below shows the ranks of the ten states/UTs mentioned above among ALL states/UTs of India in terms of the number of cases registered in each of the three category of crimes. A state/UT is given rank r for a category of crimes if there are (r‐1) states/UTs having a larger number of cases registered in that category of crimes. For example, if two states have the same number of cases in a category, and exactly three other states/UTs have larger numbers of cases registered in the same category, then both the states are given rank 4 in that category. Missing ranks in the table are denoted by *.

Q3.CAT 2019
In the two states where the highest total number of cases are registered, the ratio of the total number of cases in IPC crimes to the total number in SLL crimes is closest to
- 3 : 2
- 19 : 20
- 11 : 10
- 1 : 9
Show solution
The data can be tabulated as follows(approximately):

The highest cases are registered in West Bengal and Delhi.

The total number of IPC crimes = 63-64

The total number of SLL crimes = 520+35-36 = 555-556

Hence the ratio = (63-64)/(555-556) = 0.11 (Approximately) = 1:9
Passage
Directions for the following four questions: Answer the following questions based on the information given below: The bar chart below shows the revenue received in million US Dollars (USD), from subscribers to a particular Internet service. The data covers the period 2003 to 2007 for the United States (US) and Europe. The bar chart also shows the estimated revenues from subscription to this service for the period 2008 to 2010.

The Y axis represents the subscription revenue in Million (USD) and the X axis represents the years.
Q4.CAT 2008
Consider the annual percent change in the gap between subscription revenues in the US and Europe. What is the year in which the absolute value of this change is the highest?
- 03 - 04
- 05 - 06
- 06 - 07
- 08 - 09
- 09 - 10
Show solution
Every year, there was a comparative increase in both US and Europe subscriptions.

But in 2009, the increase in US subscriptions is very marginal and in Europe subscriptions is similar to that of any other year.

Hence, the percentage change in 2009 over 2008 would be more than any other year.
Passage
DIRECTIONS for the following three questions: Answer the questions on the basis of the information given below.

Each point in the graph below shows the profit and turnover data for a company. Each company belongs to one of the three industries: textile, cement and steel.
Q5.CAT 2003
For how many companies does the profit exceed 10% of turnover?
- 8
- 7
- 6
- 5
Show solution
There are in total 7 companies - 3 steels , 2 cement , 2 textile for which the profit is more than 10% of the turnover.
Passage
Chart 1 shows the distribution by value of top 6 suppliers of MFA Textiles in 1995.

Chart 2 shows the distribution by quantity of top 6 suppliers of MFA Textiles in 1995.

The total value is 5760 million Euro (European currency). The total quantity is 1.055 million tonnes.

Q6.CAT 2002
The country which has the highest average price is
- USA
- Switzerland
- Turkey
- India
Show solution
The country which has the highest average price would have low quality and high value when compared to other countries..

Switzerland fits the above description.

Hence, option B is the answer.
Passage
Directions for the following three questions: Answer the questions based on the pie charts given below.

Chart 1 shows the distribution of 12 million tonnes of crude oil transported through different modes over a specific period of time.

Chart 2 shows the distribution of the cost of transporting this crude oil. The total cost was Rs. 30 million.

Q7.CAT 2001
From the charts given, it appears that the cheapest mode of transport is
- road
- rail
- pipeline
- ship
Show solution
Cheapest mode of transport will be the one which will have highest transport volume and comparatively lowest cost. We can figure out from the graph that Road have wide gap with very less costs.

For Road, Cost = 6/22

For Rail, Cost = 12/9

For Pipeline, = 65/49

For Ship, Cost = 10/9

Lowest cost is for road.
Passage
These questions are based on the price fluctuations of four commodities - arhar, pepper, sugar and gold during February - July 1999 as described in the figures below:

Q8.CAT 1999
Mr. X, a funds manager with an investment company invested 25% of his funds in each of the four commodities at the beginning of the period. He sold the commodities at the end of the period. His investments in the commodities resulted in:
- 17% profit
- 5.5% loss
- no profit, no loss
- 4.3% profit
Show solution
The profit percentage equals 25%*(2105/1700-1) + 25%*(19250/18500-1) + 25%*(1430/1440-1) + 25%*(3850/4250-1)
This equals 25%*(23.82% + 4.05% -0.69% - 9.41%) = 25%*17.77 = 4.4%
The closest option to this is option (d)
Passage
Answer the questions based on the following information.

Ghosh Babu has a manufacturing unit. The following graph gives the cost for the various number of units. Given: Profit = Revenue - Variable cost - Fixed cost. The fixed cost remains constant up to 34 units after which additional investment is to be done in fixed assets. In any case, production cannot exceed 50 units.

Note: The fixed cost for upto 34 units is 50 and the the fixed cost for more is 100.
The revenue from 50 units is 1000 and the variable cost from 50 units is 700

Q9.CAT 1998
What is the least number of units that should be manufactured such that the profit was at least Rs. 50?
- 17
- 34
- 45
- 30
Show solution
The revenue of 50 units is 1000. So, the revenue per unit is 20.
The variable cost of 50 units is 700. So, the variable cost per unit is 14.

Let the minimum number of units that are needed to be produced to ensure that there is a profit of at least 50.
So, total revenue is 20X and total cost is 14X+50.
So, Profit is 20X - (14X+50) = 6X-50 > 50
Hence, 6X > 100
Or X > 16
So, the least possible number of units to be produced is 17.
Passage
Answer the questions based on the following information. In the following chart, the price of logs shown is per cubic metre that of plywood and saw timber is per tonne.

Q10.CAT 1998
If the volume sales of plywood, saw timber and logs were 40%, 30% and 30% respectively, then what was the average realisation in 1993 per cubic metre of sales? (Weight of one cubic metre of saw dust and plywood both = 800 kg)
- 18
- 15
- 16
- 13
Show solution
In 1993, price of logs = Rs. 20 per cubic metre.

volume sales of plywood, saw timber and logs were 40%, 30% and 30%
In 1993, price of plywood = Rs. 7 per tonne
In 1993, price of plywood = Rs. 20 per tonne

Weight of one cubic metre of saw dust and plywood both = 800 kg
1 tonne=1000kg
Price of 1000kg of plywood= Rs 7
Price of 800kg( 1 m $^3$ )= 7 x 0.8 = Rs 5.6 per cubic metre.
Price of saw timber = 20 x 0.8 = Rs 16 per cubic metre.

We know that the sales volume of plywood, saw timber and logs are in the ratio 4 : 3 : 3.
Thus, the average realization must be the weighted avg of these three-
$\frac{(4\times 5.6)+(3 \times 16)+(3 \times 20)}{4+3+3}$
=13.1
= Rs. 13 (Approximately)
Passage
The graph given below gives the yearly details of money invested in producing a certain product over the years 1991 to 1995. It also gives the profit (in ‘000 rupees).

Q11.CAT 1997
If the interest component is not included in the total cost calculation, which year would show the maximum profit per unit cost?
- 1991
- 1992
- 1993
- 1995
Show solution
Ratio in 1991 = $\frac{10}{120}$ = 0.833

Ratio in 1992 = $\frac{25}{125}$ = 0.2

Ratio in 1993 = $\frac{20}{145}$ = 0.138

Ratio in 1995 = $\frac{20}{160}$ = 0.125

1992 has maximum profit per unit cost.
Passage
Answer the questions based on the following information. The first table gives the percentage of students in MBA class, who sought employment in the areas of finance, marketing and software. The second table gives the average starting salaries of the students per month, (rupees in thousands) in these areas. The third table gives the number of students who passed out in each year.

Table 1:

Table 2:

Table 3:

Q12.CAT 1996
What is the average monthly salary offered to a management graduate in 1993?
- Rs. 6,403
- Rs. 6,330
- Rs. 6,333
- Cannot be determined
Show solution
As we do not know the average salary for students who did not pursue Finance, Marketing or Software jobs, we cannot find the average salary of all the students in 1993.
Hence, a unique value cannot be determined.

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CAT DI Charts Questions & Solutions

Passage

The chart below provides complete information about the number of countries visited by Dheeraj, Samantha and Nitesh, in Asia, Europe and the rest of the world (ROW).

The following additional facts are known about the countries visited by them.
1. 32 countries were visited by at least one of them.
2. USA (in ROW) is the only country that was visited by all three of them.
3. China (in Asia) is the only country that was visited by both Dheeraj and Nitesh, but not by Samantha.
4. France (in Europe) is the only country outside Asia, which was visited by both Dheeraj and Samantha, but not by Nitesh.
5. Half of the countries visited by both Samantha and Nitesh are in Europe.

Q1.CAT 2024

How many countries in Asia were visited by at least one of Dheeraj, Samantha and Nitesh?

Answer: 3

Show solution

Writing down the data with us in a table form.

But this includes countries which have been visited by one person, two people and three people. Essentially, there is an overlap of countries.
It is given to us that 32 distinct countries were visited among the three people,
Using that we can write down the equations,
$I+II+III=32$ ...(1)
$I+2II+3III=43$ ...(2)
Where I, II, and III denote the number of countries visited exactly by 1 of them, 2 of them and all of them.
We are told that USA(ROW) is the only country which was visited by all three people, that means $III=1$

Subtracting Equation 1 from 2 we get, $II+2III=11$
And since III=1 we get $II=9$

So, we are looking for 9 countries visited by exactly 2 people, and 22 countries visited by exactly 1 person.
Using the information from the problem set, we can note down the following,

We can see that Dheeraj visited only 1 country in ROW so every other value in that column has to be zero for wherever Dinesh is present. And Samantha has not visited any country in Asia so every value with Samantha present in Asia should be zero as well.

We have the following distribution, we are looking for 9 countries visited by exactly 2 people. And we have identified 2 countries, that means, 7 were countries were visited by both Samantha and Nitesh only. And given that half the countries visited by both of them are in Europe, and total number of countries visited by both of them is 7(only two of them)+1(USA)=8, they visited 4 countries in Europe together and 3 countries in ROW together. And using that information, we can fill in the rest of the table as well. Since we know the number of countries visited by each of them in a particular continent.

How many countries in Asia were visited by at least one of Dheeraj, Samantha and Nitesh is 3.

Passage

Comprehension:
Over the top (OTT) subscribers of a platform are segregated into three categories: i) Kid, ii)Elder, and iii) Others. Some of the subscribers used one app and the others used multiple apps to access the platform. The figure below shows the percentage of the total number of subscribers in 2023 and 2024 who belong to the ‘Kid’ and ‘Elder’ categories.

The following additional facts are known about the numbers of subscribers.
1. The total number of subscribers increased by 10% from 2023 to 2024.
2. In 2024, 1/2 of the subscribers from the ‘Kid’ category and 2/3 of the subscribers from the ‘Elder’ category subscribers use one app.
3. In 2023, the number of subscribers from the ‘Kid’ category who used multiple apps was the same as the number of subscribers from the ‘Elder’ category who used one app.
4. 10,000 subscribers from the ‘Kid’ category used one app and 15,000 subscribers from the ‘Elder’ category used multiple apps in 2023.

Q2.CAT 2024

How many subscribers belonged to the ‘Others’ category in 2024?

Cannot be determined
65000
55000
45000

Show solution

Reading the bar graphs, we can find the distribution of the subscribers as:

Taking clue one into consideration, let's take the total number of subscribers in 2023 as 100x and in 2204 as 110x
This would give the split of subscribers as follows:

Clue 2 says that half of 22x, which is 11x and 2/3 of 33x, which is 22x, used one app, given that in 2024, out of 55x, 33x used one app.

Clues 3 and 4 are to be used with each other.
Clue 4 says that out of 15x kids, 10,000 used one app, and out of 20x Elders, 15,000 used multiple apps.
Clue 3 says that the kids who used multiple apps (15x - 10000) were the same as Elders who used one app (20x - 15000)

Equating these two we get:
15x- 10000 = 20x - 15000
5x = 5000
x = 1000

The first question asks about the number of others in 2024, which is 55x, or simply 55,000

Therefore, Option C is the correct answer.

Passage

The Ministry of Home Affairs is analysing crimes committed by foreigners in different states and union territories (UT) of India. All cases refer to the ones registered against foreigners in 2016.

The number of cases - classified into three categories: IPC crimes, SLL crimes and other crimes - for nine states/UTs are shown in the figure below. These nine belong to the top ten states/UTs in terms of the total number of cases registered. The remaining state (among top ten) is West Bengal, where all the 520 cases registered were SLL crimes.

The table below shows the ranks of the ten states/UTs mentioned above among ALL states/UTs of India in terms of the number of cases registered in each of the three category of crimes. A state/UT is given rank r for a category of crimes if there are (r‐1) states/UTs having a larger number of cases registered in that category of crimes. For example, if two states have the same number of cases in a category, and exactly three other states/UTs have larger numbers of cases registered in the same category, then both the states are given rank 4 in that category. Missing ranks in the table are denoted by *.

Q3.CAT 2019

In the two states where the highest total number of cases are registered, the ratio of the total number of cases in IPC crimes to the total number in SLL crimes is closest to

3 : 2
19 : 20
11 : 10
1 : 9

Show solution

The data can be tabulated as follows(approximately):

The highest cases are registered in West Bengal and Delhi.

The total number of IPC crimes = 63-64

The total number of SLL crimes = 520+35-36 = 555-556

Hence the ratio = (63-64)/(555-556) = 0.11 (Approximately) = 1:9

Passage

Directions for the following four questions: Answer the following questions based on the information given below: The bar chart below shows the revenue received in million US Dollars (USD), from subscribers to a particular Internet service. The data covers the period 2003 to 2007 for the United States (US) and Europe. The bar chart also shows the estimated revenues from subscription to this service for the period 2008 to 2010.

The Y axis represents the subscription revenue in Million (USD) and the X axis represents the years.

Q4.CAT 2008

Consider the annual percent change in the gap between subscription revenues in the US and Europe. What is the year in which the absolute value of this change is the highest?

03 - 04
05 - 06
06 - 07
08 - 09
09 - 10

Show solution

Every year, there was a comparative increase in both US and Europe subscriptions.

But in 2009, the increase in US subscriptions is very marginal and in Europe subscriptions is similar to that of any other year.

Hence, the percentage change in 2009 over 2008 would be more than any other year.

Passage

DIRECTIONS for the following three questions: Answer the questions on the basis of the information given below.

Each point in the graph below shows the profit and turnover data for a company. Each company belongs to one of the three industries: textile, cement and steel.

Q5.CAT 2003

For how many companies does the profit exceed 10% of turnover?

Show solution

There are in total 7 companies - 3 steels , 2 cement , 2 textile for which the profit is more than 10% of the turnover.

Passage

Chart 1 shows the distribution by value of top 6 suppliers of MFA Textiles in 1995.

Chart 2 shows the distribution by quantity of top 6 suppliers of MFA Textiles in 1995.

The total value is 5760 million Euro (European currency). The total quantity is 1.055 million tonnes.

Q6.CAT 2002

The country which has the highest average price is

USA
Switzerland
Turkey
India

Show solution

The country which has the highest average price would have low quality and high value when compared to other countries..

Switzerland fits the above description.

Hence, option B is the answer.

Passage

Directions for the following three questions: Answer the questions based on the pie charts given below.

Chart 1 shows the distribution of 12 million tonnes of crude oil transported through different modes over a specific period of time.

Chart 2 shows the distribution of the cost of transporting this crude oil. The total cost was Rs. 30 million.

Q7.CAT 2001

From the charts given, it appears that the cheapest mode of transport is

road
rail
pipeline
ship

Show solution

Cheapest mode of transport will be the one which will have highest transport volume and comparatively lowest cost. We can figure out from the graph that Road have wide gap with very less costs.

For Road, Cost = 6/22

For Rail, Cost = 12/9

For Pipeline, = 65/49

For Ship, Cost = 10/9

Lowest cost is for road.

Passage

These questions are based on the price fluctuations of four commodities - arhar, pepper, sugar and gold during February - July 1999 as described in the figures below:

Q8.CAT 1999

Mr. X, a funds manager with an investment company invested 25% of his funds in each of the four commodities at the beginning of the period. He sold the commodities at the end of the period. His investments in the commodities resulted in:

17% profit
5.5% loss
no profit, no loss
4.3% profit

Show solution

The profit percentage equals 25%*(2105/1700-1) + 25%*(19250/18500-1) + 25%*(1430/1440-1) + 25%*(3850/4250-1)
This equals 25%*(23.82% + 4.05% -0.69% - 9.41%) = 25%*17.77 = 4.4%

The closest option to this is option (d)

Passage

Answer the questions based on the following information.

Ghosh Babu has a manufacturing unit. The following graph gives the cost for the various number of units. Given: Profit = Revenue - Variable cost - Fixed cost. The fixed cost remains constant up to 34 units after which additional investment is to be done in fixed assets. In any case, production cannot exceed 50 units.

Note: The fixed cost for upto 34 units is 50 and the the fixed cost for more is 100.
The revenue from 50 units is 1000 and the variable cost from 50 units is 700

Q9.CAT 1998

What is the least number of units that should be manufactured such that the profit was at least Rs. 50?

Show solution

The revenue of 50 units is 1000. So, the revenue per unit is 20.
The variable cost of 50 units is 700. So, the variable cost per unit is 14.

Let the minimum number of units that are needed to be produced to ensure that there is a profit of at least 50.
So, total revenue is 20X and total cost is 14X+50.
So, Profit is 20X - (14X+50) = 6X-50 > 50
Hence, 6X > 100
Or X > 16
So, the least possible number of units to be produced is 17.

Passage

Answer the questions based on the following information. In the following chart, the price of logs shown is per cubic metre that of plywood and saw timber is per tonne.

Q10.CAT 1998

If the volume sales of plywood, saw timber and logs were 40%, 30% and 30% respectively, then what was the average realisation in 1993 per cubic metre of sales? (Weight of one cubic metre of saw dust and plywood both = 800 kg)

Show solution

In 1993, price of logs = Rs. 20 per cubic metre.

volume sales of plywood, saw timber and logs were 40%, 30% and 30%

In 1993, price of plywood = Rs. 7 per tonne

In 1993, price of plywood = Rs. 20 per tonne

Weight of one cubic metre of saw dust and plywood both = 800 kg

1 tonne=1000kg

Price of 1000kg of plywood= Rs 7

Price of 800kg( 1 m $^3$ )= 7 x 0.8 = Rs 5.6 per cubic metre.

Price of saw timber = 20 x 0.8 = Rs 16 per cubic metre.

We know that the sales volume of plywood, saw timber and logs are in the ratio 4 : 3 : 3.
Thus, the average realization must be the weighted avg of these three-
$\frac{(4\times 5.6)+(3 \times 16)+(3 \times 20)}{4+3+3}$
=13.1
= Rs. 13 (Approximately)

Passage

The graph given below gives the yearly details of money invested in producing a certain product over the years 1991 to 1995. It also gives the profit (in ‘000 rupees).

Q11.CAT 1997

If the interest component is not included in the total cost calculation, which year would show the maximum profit per unit cost?

1991
1992
1993
1995

Show solution

Ratio in 1991 = $\frac{10}{120}$ = 0.833

Ratio in 1992 = $\frac{25}{125}$ = 0.2

Ratio in 1993 = $\frac{20}{145}$ = 0.138

Ratio in 1995 = $\frac{20}{160}$ = 0.125

1992 has maximum profit per unit cost.

Passage

Answer the questions based on the following information. The first table gives the percentage of students in MBA class, who sought employment in the areas of finance, marketing and software. The second table gives the average starting salaries of the students per month, (rupees in thousands) in these areas. The third table gives the number of students who passed out in each year.

Table 1:

Table 2:

Table 3:

Q12.CAT 1996

What is the average monthly salary offered to a management graduate in 1993?

Rs. 6,403
Rs. 6,330
Rs. 6,333
Cannot be determined

Show solution

As we do not know the average salary for students who did not pursue Finance, Marketing or Software jobs, we cannot find the average salary of all the students in 1993.

Hence, a unique value cannot be determined.

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