Interpretation of Data Questions and Answers

Q: How many villages were visited by both the salesmen ?

8 villages were visited by both salesmen.Two of the 20 villages were visited by neither, so 18 were visited by at least one. By the inclusion-exclusion principle:\[ \begin{aligned} n(A \cup B) &= n(A) + n(B) - n(A \cap B) \\ 18 &= 14 + 12 - n(A \cap B) \\ n(A \cap B) &= 8 \end{aligned} \]The option 26 simply adds 14 and 12, counting the shared villages twice; 6 is the number visited by A alone (14 - 8), and 4 the number visited by B alone (12 - 8).

Q: How many villages were visited by at least one salesman ?

18 villages were visited by at least one salesman.There are 20 villages, and 2 of them were visited by neither salesman. Every other village was visited by A, by B or by both, so the number visited by at least one is 20 - 2 = 18.As a check: 14 + 12 - 8 = 18, using the 8 villages both of them visited. The option 26 is 14 + 12, which counts those 8 twice, and 20 forgets the 2 villages that neither visited.

Q: The information in the above table is to be represented diagrammatically using Pie diagram. What will be the angle of the sector representing item labour ?

The labour sector has an angle of 90°.In a pie diagram the whole, 100 per cent, is the full circle of 360°, so each per cent is 3.6°.\[ 25 \times 3.6^{\circ} = 90^{\circ} \]25° copies the percentage without converting it, and 30° and 50° do not correspond to 25 per cent of the circle.

Q: What is the ratio of expenditure of the item cement and bricks to the total expenditure of construction of house ?

The ratio is 3 : 10.Cement and bricks account for 30 per cent of the total expenditure, that is 30 out of 100.\[ 30 : 100 = 3 : 10 \]1 : 3 would be about 33 per cent and 1 : 4 is 25 per cent, which is labour's share; 2 : 5 would be 40 per cent.

Q: What is percentage of total number of tourists visiting Agra ?

Agra's share is 25.00%.The total for all places is 15.0 + 20.0 + 10.0 + 6.0 + 6.0 + 3.0 = 60.0 lakh tourists, of whom 15.0 lakh visited Agra.\[ \frac{15}{60} \times 100 = 25\% \]33.33% is Delhi's share (20 of 60), 16.67% is Chennai's (10 of 60), and 10.00% is Udaipur's or Bangalore's (6 of 60).

Q: Which type of tourists found maximum at Delhi ?

The largest group at Delhi is English.Delhi's row shows 8.2 lakh American, 8.7 lakh English, 2.7 lakh French and 0.4 lakh other tourists. English tourists (8.7) are the most numerous, just ahead of Americans (8.2).Americans are the largest group at most other places in the table, which is the trap; at Delhi the English outnumber them.

Q: Find the angle in degrees associated with sector 'other'.

The angle for 'other' is 90°.The angles of a pie chart add up to 360°:\[ \begin{aligned} x &= 360 - (108 + 63 + 72 + 27) \\ &= 360 - 270 = 90^\circ \end{aligned} \]63°, 108° and 72° are the angles already given for clothing, food and house rent, not the remaining sector.

Q: Find the percentage of expenses on sector 'Food' :

Food accounts for 30% of the expenses.A sector's share of the total is its angle divided by 360°:\[ \frac{108}{360} \times 100 = 30\% \]25% would be a 90° sector, the 'other' expenses, and 20% a 72° sector, house rent. 90% confuses the 'other' sector's angle with a percentage.

Q: For which type of industry the difference between the companies of districts E and B is maximum ?

The difference is maximum for Engineering and allied.Subtract district B from district E for each type:\[ \begin{aligned} \text{Agro} &: 165 - 86 = 79 \\ \text{Forest} &: 120 - 70 = 50 \\ \text{Livestock} &: 176 - 90 = 86 \\ \text{Textile} &: 132 - 92 = 40 \\ \text{Chemical} &: 154 - 86 = 68 \\ \text{Engineering} &: 166 - 76 = 90 \end{aligned} \]The largest difference, 90, is for engineering and allied. Agro-based (79) and chemical-based (68) are smaller, and textile-based has the smallest difference of all.

Q: What is the percentage of agro-based industries in district B ?

The percentage is 17.2%.District B has 86 agro-based companies out of a total of 500:\[ \frac{86}{500} \times 100 = 17.2\% \]86% treats the count as a percentage, 8.6% divides by 1000 instead of 500, and 16.67% would be one-sixth, the share if all six types were equal.

Direction for [ Question No: 21 To 22 ] :

The following questions are based on the following information :

Out of 20 villages in a certain state, salesman A visited 14 villages, salesman B visited 12 villages. None of them visited 2 villages.

21.

How many villages were visited by both the salesmen ?

A.26
B.6
C.4
D.8

Exam Year(s)

MH SET - 2025, SET Exam - 2025,

Answer: D

8 villages were visited by both salesmen.

Two of the 20 villages were visited by neither, so 18 were visited by at least one. By the inclusion-exclusion principle:

\[ \begin{aligned} n(A \cup B) &= n(A) + n(B) - n(A \cap B) \\ 18 &= 14 + 12 - n(A \cap B) \\ n(A \cap B) &= 8 \end{aligned} \]

The option 26 simply adds 14 and 12, counting the shared villages twice; 6 is the number visited by A alone (14 - 8), and 4 the number visited by B alone (12 - 8).

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22.

How many villages were visited by at least one salesman ?

A.26
B.18
C.20
D.8

Exam Year(s)

MH SET - 2025, SET Exam - 2025,

Answer: B

18 villages were visited by at least one salesman.

There are 20 villages, and 2 of them were visited by neither salesman. Every other village was visited by A, by B or by both, so the number visited by at least one is 20 - 2 = 18.

As a check: 14 + 12 - 8 = 18, using the 8 villages both of them visited. The option 26 is 14 + 12, which counts those 8 twice, and 20 forgets the 2 villages that neither visited.

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Direction for [ Question No: 23 To 24 ] :

The following questions are based on the following information :

Following table gives itemwise expenditure of construction of house.

Item	Expenditure (%)
Labour	25
Cement and Bricks	30
Steel	15
Timber and Glass	20
Miscellaneous	10

23.

The information in the above table is to be represented diagrammatically using Pie diagram. What will be the angle of the sector representing item labour ?

A.50°
B.30°
C.90°
D.25°

Exam Year(s)

MH SET - 2024, SET Exam - 2024,

Answer: C

The labour sector has an angle of 90°.

In a pie diagram the whole, 100 per cent, is the full circle of 360°, so each per cent is 3.6°.

\[ 25 \times 3.6^{\circ} = 90^{\circ} \]

25° copies the percentage without converting it, and 30° and 50° do not correspond to 25 per cent of the circle.

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24.

What is the ratio of expenditure of the item cement and bricks to the total expenditure of construction of house ?

A.1 : 3
B.1 : 4
C.2 : 5
D.3 : 10

Exam Year(s)

MH SET - 2024, SET Exam - 2024,

Answer: D

The ratio is 3 : 10.

Cement and bricks account for 30 per cent of the total expenditure, that is 30 out of 100.

\[ 30 : 100 = 3 : 10 \]

1 : 3 would be about 33 per cent and 1 : 4 is 25 per cent, which is labour's share; 2 : 5 would be 40 per cent.

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Direction for [ Question No: 25 To 26 ] :

The following questions are based on the following information :

Following is a table representing foreign tourists visiting different places in India in a certain year. (Figures are in lakhs).

Place / Type	American	English	French	Other	Total
Agra	6.5	3.8	3.5	1.2	15.0
Delhi	8.2	8.7	2.7	0.4	20.0
Chennai	3.7	3.3	2.4	0.6	10.0
Udaipur	2.8	1.3	1.5	0.4	6.0
Bangalore	3.0	1.2	1.3	0.5	6.0
Shrinagar	1.0	0.8	1.1	0.1	3.0

25.

What is percentage of total number of tourists visiting Agra ?

A.33.33%
B.25.00%
C.16.67%
D.10.00%

Exam Year(s)

MH SET - 2024, SET Exam - 2024,

Answer: B

Agra's share is 25.00%.

The total for all places is 15.0 + 20.0 + 10.0 + 6.0 + 6.0 + 3.0 = 60.0 lakh tourists, of whom 15.0 lakh visited Agra.

\[ \frac{15}{60} \times 100 = 25\% \]

33.33% is Delhi's share (20 of 60), 16.67% is Chennai's (10 of 60), and 10.00% is Udaipur's or Bangalore's (6 of 60).

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26.

Which type of tourists found maximum at Delhi ?

A.American
B.English
C.French
D.Other

Exam Year(s)

MH SET - 2024, SET Exam - 2024,

Answer: B

The largest group at Delhi is English.

Delhi's row shows 8.2 lakh American, 8.7 lakh English, 2.7 lakh French and 0.4 lakh other tourists. English tourists (8.7) are the most numerous, just ahead of Americans (8.2).

Americans are the largest group at most other places in the table, which is the trap; at Delhi the English outnumber them.

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Direction for [ Question No: 27 To 28 ] :

The following questions are based on the following information :

Monthly expenses on various items of a certain family are shown in the following diagram (a pie chart; the sector angles are given below) :

Item	Sector angle
Food	108°
Clothing	63°
House rent	72°
Fuel etc.	27°
Other	x°

27.

Find the angle in degrees associated with sector 'other'.

A.63°
B.90°
C.108°
D.72°

Exam Year(s)

MH SET - 2023, SET Exam - 2023,

Answer: B

The angle for 'other' is 90°.

The angles of a pie chart add up to 360°:

\[ \begin{aligned} x &= 360 - (108 + 63 + 72 + 27) \\ &= 360 - 270 = 90^\circ \end{aligned} \]

63°, 108° and 72° are the angles already given for clothing, food and house rent, not the remaining sector.

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28.

Find the percentage of expenses on sector 'Food' :

A.25%
B.30%
C.20%
D.90%

Exam Year(s)

MH SET - 2023, SET Exam - 2023,

Answer: B

Food accounts for 30% of the expenses.

A sector's share of the total is its angle divided by 360°:

\[ \frac{108}{360} \times 100 = 30\% \]

25% would be a 90° sector, the 'other' expenses, and 20% a 72° sector, house rent. 90% confuses the 'other' sector's angle with a percentage.

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Direction for [ Question No: 29 To 30 ] :

The following questions are based on the following information :

The following is the distribution of number of companies of different types in different districts of a state :

Types of Industries	A	B	C	D	E
Agro-based	90	86	132	45	165
Forest-based	105	70	101	30	120
Livestock-based	87	90	100	42	176
Textile-based	80	92	142	36	132
Chemical-based	88	86	108	36	154
Engineering and allied	98	76	117	40	166
Total	548	500	700	229	913

(A to E are the Districts.)

29.

For which type of industry the difference between the companies of districts E and B is maximum ?

A.Engineering and allied
B.Agro-based
C.Chemical-based
D.Textile-based

Exam Year(s)

MH SET - 2023, SET Exam - 2023,

Answer: A

The difference is maximum for Engineering and allied.

Subtract district B from district E for each type:

\[ \begin{aligned} \text{Agro} &: 165 - 86 = 79 \\ \text{Forest} &: 120 - 70 = 50 \\ \text{Livestock} &: 176 - 90 = 86 \\ \text{Textile} &: 132 - 92 = 40 \\ \text{Chemical} &: 154 - 86 = 68 \\ \text{Engineering} &: 166 - 76 = 90 \end{aligned} \]

The largest difference, 90, is for engineering and allied. Agro-based (79) and chemical-based (68) are smaller, and textile-based has the smallest difference of all.

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30.

What is the percentage of agro-based industries in district B ?

A.86%
B.17.2%
C.8.6%
D.16.67%

Exam Year(s)

MH SET - 2023, SET Exam - 2023,

Answer: B

The percentage is 17.2%.

District B has 86 agro-based companies out of a total of 500:

\[ \frac{86}{500} \times 100 = 17.2\% \]

86% treats the count as a percentage, 8.6% divides by 1000 instead of 500, and 16.67% would be one-sixth, the share if all six types were equal.

Interpretation of Data Questions and Answers

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Direction for [ Question No: 23 To 24 ] :

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Direction for [ Question No: 27 To 28 ] :

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Interpretation of Data Questions and Answers

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