Interpretation of Data Questions and Answers

Q: Which employee has maximum working days during the years 2018-2022 ?

The employee with the most working days is E.Add each column over the five years:A: 280 + 300 + 310 + 315 + 295 = 1500B: 310 + 290 + 300 + 310 + 300 = 1510C: 315 + 310 + 315 + 315 + 300 = 1555D: 315 + 315 + 310 + 310 + 305 = 1555E: 320 + 325 + 320 + 330 + 310 = 1605E has the highest total, 1605. E also has the highest figure in every single year, which confirms the result without the full addition.

Q: Which employees have equal number of total working days during 2018-2022 ?

The employees with equal totals are C and D.The five-year totals are A 1500, B 1510, C 1555, D 1555 and E 1605. Only C and D are equal, at 1555 each.A and B differ by 10 (1500 against 1510), B and D by 45, and A, B and C are all different. So every option other than 'C and D' names employees whose totals do not match.

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.

Direction for [ Question No: 1 To 2 ] :

The following questions are based on the following information :

Number of working days annually :

Year	Employee
Year	A	B	C	D	E
2018	280	310	315	315	320
2019	300	290	310	315	325
2020	310	300	315	310	320
2021	315	310	315	310	330
2022	295	300	300	305	310

Which employee has maximum working days during the years 2018-2022 ?

Exam Year(s)

MH SET - 2025, SET Exam - 2025,

Answer: D

The employee with the most working days is E.

Add each column over the five years:

A: 280 + 300 + 310 + 315 + 295 = 1500
B: 310 + 290 + 300 + 310 + 300 = 1510
C: 315 + 310 + 315 + 315 + 300 = 1555
D: 315 + 315 + 310 + 310 + 305 = 1555
E: 320 + 325 + 320 + 330 + 310 = 1605

E has the highest total, 1605. E also has the highest figure in every single year, which confirms the result without the full addition.

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Which employees have equal number of total working days during 2018-2022 ?

A.A and B
B.C and D
C.A, B and C
D.B and D

Exam Year(s)

MH SET - 2025, SET Exam - 2025,

Answer: B

The employees with equal totals are C and D.

The five-year totals are A 1500, B 1510, C 1555, D 1555 and E 1605. Only C and D are equal, at 1555 each.

A and B differ by 10 (1500 against 1510), B and D by 45, and A, B and C are all different. So every option other than 'C and D' names employees whose totals do not match.

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Direction for [ Question No: 3 To 4 ] :

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.

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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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: 5 To 6 ] :

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

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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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: 7 To 8 ] :

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

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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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: 9 To 10 ] :

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°

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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10.

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.

Interpretation of Data Questions and Answers

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