Interpretation of Data Questions and Answers

Q: How many players are playing only one game ?

61 players play only one game.Those in exactly two games are the pairwise figures minus the 3 who play all three:\[ \begin{aligned} \text{two} &= (8-3) + (10-3) + (7-3) = 16 \\ \text{union} &= 102 - (8 + 10 + 7) + 3 = 80 \\ \text{one} &= 80 - 16 - 3 = 61 \end{aligned} \]The union equals the 80 players, so everyone plays at least one game. 102 is the plain sum 35 + 42 + 25 without removing overlaps, 80 is everyone, and 63 does not match any count that can be formed from the figures given, such as one game (61) or two games (16).

Q: How many players play exactly two games ?

16 players play exactly two games.Each pairwise figure includes the 3 players who play all three games, so subtract them from each pair:\[ \begin{aligned} \text{C and H only} &= 8 - 3 = 5 \\ \text{C and F only} &= 10 - 3 = 7 \\ \text{H and F only} &= 7 - 3 = 4 \\ \text{total} &= 5 + 7 + 4 = 16 \end{aligned} \]19 is that total plus the 3 who play all three games. 61 is the number who play only one game, and 80 is all the players.

Q: In which year is the percentage of passing of students maximum ?

The pass percentage is highest in 2015.\[ \begin{aligned} 2012: \frac{200}{500} &= 40\% \\ 2013: \frac{400}{700} &\approx 57.1\% \\ 2014: \frac{500}{800} &= 62.5\% \\ 2015: \frac{700}{1000} &= 70\% \end{aligned} \]The pass rate rises every year, reaching 70% in 2015. 2014 has more passes than 2013 but a lower rate than 2015, and 2012 is the lowest at 40%. Read the hatched part of each bar as the passes, not the whole bar.

Q: The percentage of passing of students in examination for all the years 2012 to 2015 combined together is ..................... .

The combined pass percentage is 60.Add the passes and the totals over all four years before dividing:\[ \begin{aligned} \text{passed} &= 200 + 400 + 500 + 700 = 1800 \\ \text{total} &= 500 + 700 + 800 + 1000 = 3000 \\ \frac{1800}{3000} &= 60\% \end{aligned} \]Averaging the four yearly rates instead gives about 57.4%, close to the 57.14 option, which is only 2013's rate. 70 is 2015's rate alone, and 50 has no basis in the data.

Q: How many students failed in exactly two languages ?

165 students failed in exactly two languages.Each 'failed in both' figure includes the 30 who failed in all three, so subtract 30 from each pair:\[ \begin{aligned} \text{M and E only} &= 125 - 30 = 95 \\ \text{M and H only} &= 70 - 30 = 40 \\ \text{E and H only} &= 60 - 30 = 30 \\ \text{total} &= 95 + 40 + 30 = 165 \end{aligned} \]255 is the raw sum 125 + 70 + 60, which counts the all-three group three times, and 195 subtracts the 30 only twice instead of three times. 250 is the number who failed in only one language (Q34).

Q: How many failed in only one language ?

250 students failed in only one language.For each language subtract the two pairs that include it and add back the 30 who were subtracted twice:\[ \begin{aligned} \text{Marathi only} &= 220 - 125 - 70 + 30 = 55 \\ \text{English only} &= 300 - 125 - 60 + 30 = 145 \\ \text{Hindi only} &= 150 - 70 - 60 + 30 = 50 \\ \text{total} &= 55 + 145 + 50 = 250 \end{aligned} \]Check: 250 in one language, 165 in exactly two and 30 in all three make 445 who failed at least once, which agrees with \(670 - 255 + 30 = 445\). 165 is the exactly-two count, and 195 and 255 are wrong pair totals.

Q: In which year the revenue generated per unit exported is maximum ?

Revenue per unit exported is highest in 2012.Divide the revenue by the quantity for each year. Revenue is in crores and quantity in lakhs, and one crore is 100 lakh, so crores per lakh units times 100 gives rupees per unit:\[ \begin{aligned} 2011 &: 20/10 \times 100 = 200 \\ 2012 &: 15/5 \times 100 = 300 \\ 2013 &: 35/15 \times 100 \approx 233 \\ 2014 &: 40/20 \times 100 = 200 \\ 2015 &: 50/30 \times 100 \approx 167 \end{aligned} \]2012 has the smallest export of the five years but the highest return per unit, Rs. 300. 2015 has the largest revenue and quantity, but the lowest revenue per unit, and 2013 and 2014 fall in between.

Q: What is the average (arithmetic mean) per unit revenue generated during 2011 to 2015 :

The key's answer is Rs. 200, the average revenue per unit over the whole period.Taking the five years together, divide total revenue by total quantity exported:\[ \begin{aligned} \text{revenue} &= 20+15+35+40+50 = 160\ \text{crore} \\ \text{quantity} &= 10+5+15+20+30 = 80\ \text{lakh} \\ \text{per unit} &= \tfrac{160}{80} \times 100 = \text{Rs. } 200 \end{aligned} \]Averaging the five yearly figures instead (200, 300, 233, 200 and 167) would give about Rs. 220, which is not among the options, so the key uses the overall ratio. Rs. 166, Rs. 233 and Rs. 300 are the single-year figures for 2015, 2013 and 2012.

Q: If the cost of paper is Rs. 16,000, then find the amount of other charges :

The other charges amount to Rs. 8,000.The shares must total 100%, so other charges are \(x = 100 - (35 + 20 + 15 + 20) = 10\%\). Paper is 20% and costs Rs. 16,000:\[ \begin{aligned} \text{total} &= 16000 \div 0.20 = 80000 \\ \text{other} &= 10\% \times 80000 = 8000 \end{aligned} \]Rs. 16,000 assumes other charges equal paper, and Rs. 12,000 is the royalty (15%), not the other charges.

Q: The tax deducted at source is 10% of the royalty amount then the amount of tax paid is ............... .

The tax paid is Rs. 1,200.From the same pie-diagram, the total cost is Rs. 80,000 (paper, 20%, is Rs. 16,000), and royalty is 15% of it.\[ \begin{aligned} \text{royalty} &= 15\% \times 80000 = 12000 \\ \text{TDS} &= 10\% \times 12000 = 1200 \end{aligned} \]Rs. 800 is 10% of the other charges, Rs. 1,000 is a rounded guess, and Rs. 8,000 is the other charges themselves.

Direction for [ Question No: 1 To 2 ] :

Directions : The following questions are based on the following information :

Out of 80 players 35 play cricket, 42 play hockey, 25 play football, 8 play both cricket and hockey, 10 play both cricket and football, 7 play both hockey and football, 3 play all the three games.

How many players are playing only one game ?

A.102
B.80
C.61
D.63

Exam Year(s)

MH SET - 2021, SET Exam - 2021,

Answer: C

61 players play only one game.

Those in exactly two games are the pairwise figures minus the 3 who play all three:

\[ \begin{aligned} \text{two} &= (8-3) + (10-3) + (7-3) = 16 \\ \text{union} &= 102 - (8 + 10 + 7) + 3 = 80 \\ \text{one} &= 80 - 16 - 3 = 61 \end{aligned} \]

The union equals the 80 players, so everyone plays at least one game. 102 is the plain sum 35 + 42 + 25 without removing overlaps, 80 is everyone, and 63 does not match any count that can be formed from the figures given, such as one game (61) or two games (16).

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How many players play exactly two games ?

A.19
B.61
C.80
D.16

Exam Year(s)

MH SET - 2021, SET Exam - 2021,

Answer: D

16 players play exactly two games.

Each pairwise figure includes the 3 players who play all three games, so subtract them from each pair:

\[ \begin{aligned} \text{C and H only} &= 8 - 3 = 5 \\ \text{C and F only} &= 10 - 3 = 7 \\ \text{H and F only} &= 7 - 3 = 4 \\ \text{total} &= 5 + 7 + 4 = 16 \end{aligned} \]

19 is that total plus the 3 who play all three games. 61 is the number who play only one game, and 80 is all the players.

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Direction for [ Question No: 3 To 4 ] :

Directions : The following questions are based on the following diagram :

The following is a diagram of a certain college showing the number of students passed and failed during the years 2012 to 2015 :

Year	Number of Students (total)	Passed
2012	500	200
2013	700	400
2014	800	500
2015	1000	700

(The diagram is a stacked bar chart: each bar shows the total, with the passed students as the lower, hatched part and the failed students above it.)

In which year is the percentage of passing of students maximum ?

A.2012
B.2013
C.2014
D.2015

Exam Year(s)

MH SET - 2021, SET Exam - 2021,

Answer: D

The pass percentage is highest in 2015.

\[ \begin{aligned} 2012: \frac{200}{500} &= 40\% \\ 2013: \frac{400}{700} &\approx 57.1\% \\ 2014: \frac{500}{800} &= 62.5\% \\ 2015: \frac{700}{1000} &= 70\% \end{aligned} \]

The pass rate rises every year, reaching 70% in 2015. 2014 has more passes than 2013 but a lower rate than 2015, and 2012 is the lowest at 40%. Read the hatched part of each bar as the passes, not the whole bar.

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The percentage of passing of students in examination for all the years 2012 to 2015 combined together is ..................... .

A.50
B.57.14
C.60
D.70

Exam Year(s)

MH SET - 2021, SET Exam - 2021,

Answer: C

The combined pass percentage is 60.

Add the passes and the totals over all four years before dividing:

\[ \begin{aligned} \text{passed} &= 200 + 400 + 500 + 700 = 1800 \\ \text{total} &= 500 + 700 + 800 + 1000 = 3000 \\ \frac{1800}{3000} &= 60\% \end{aligned} \]

Averaging the four yearly rates instead gives about 57.4%, close to the 57.14 option, which is only 2013's rate. 70 is 2015's rate alone, and 50 has no basis in the data.

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Direction for [ Question No: 5 To 6 ] :

The following questions are based on the following information :

Among 800 students 220 failed in Marathi, 300 failed in English, 150 failed in Hindi, 125 failed in both Marathi and English, 70 failed in both Marathi and Hindi, 60 failed in both English and Hindi. 30 failed in all the three languages.

How many students failed in exactly two languages ?

A.195
B.165
C.250
D.255

Exam Year(s)

MH SET - 2020, SET Exam - 2020,

Answer: B

165 students failed in exactly two languages.

Each 'failed in both' figure includes the 30 who failed in all three, so subtract 30 from each pair:

\[ \begin{aligned} \text{M and E only} &= 125 - 30 = 95 \\ \text{M and H only} &= 70 - 30 = 40 \\ \text{E and H only} &= 60 - 30 = 30 \\ \text{total} &= 95 + 40 + 30 = 165 \end{aligned} \]

255 is the raw sum 125 + 70 + 60, which counts the all-three group three times, and 195 subtracts the 30 only twice instead of three times. 250 is the number who failed in only one language (Q34).

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How many failed in only one language ?

A.195
B.165
C.250
D.255

Exam Year(s)

MH SET - 2020, SET Exam - 2020,

Answer: C

250 students failed in only one language.

For each language subtract the two pairs that include it and add back the 30 who were subtracted twice:

\[ \begin{aligned} \text{Marathi only} &= 220 - 125 - 70 + 30 = 55 \\ \text{English only} &= 300 - 125 - 60 + 30 = 145 \\ \text{Hindi only} &= 150 - 70 - 60 + 30 = 50 \\ \text{total} &= 55 + 145 + 50 = 250 \end{aligned} \]

Check: 250 in one language, 165 in exactly two and 30 in all three make 445 who failed at least once, which agrees with \(670 - 255 + 30 = 445\). 165 is the exactly-two count, and 195 and 255 are wrong pair totals.

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Direction for [ Question No: 7 To 8 ] :

The following questions are based on the following diagram :

The following is a diagram of a company ABC showing the quantity of a certain goods exported in lakh units and the revenue generated in crores of rupees for the years 2011 to 2015 :

Year	Quantity exported (lakh units)	Revenue generated (crore rupees)
2011	10	20
2012	5	15
2013	15	35
2014	20	40
2015	30	50

In which year the revenue generated per unit exported is maximum ?

A.2012
B.2013
C.2014
D.2015

Exam Year(s)

MH SET - 2020, SET Exam - 2020,

Answer: A

Revenue per unit exported is highest in 2012.

Divide the revenue by the quantity for each year. Revenue is in crores and quantity in lakhs, and one crore is 100 lakh, so crores per lakh units times 100 gives rupees per unit:

\[ \begin{aligned} 2011 &: 20/10 \times 100 = 200 \\ 2012 &: 15/5 \times 100 = 300 \\ 2013 &: 35/15 \times 100 \approx 233 \\ 2014 &: 40/20 \times 100 = 200 \\ 2015 &: 50/30 \times 100 \approx 167 \end{aligned} \]

2012 has the smallest export of the five years but the highest return per unit, Rs. 300. 2015 has the largest revenue and quantity, but the lowest revenue per unit, and 2013 and 2014 fall in between.

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What is the average (arithmetic mean) per unit revenue generated during 2011 to 2015 :

A.Rs. 166
B.Rs. 200
C.Rs. 233
D.Rs. 300

Exam Year(s)

MH SET - 2020, SET Exam - 2020,

Answer: B

The key's answer is Rs. 200, the average revenue per unit over the whole period.

Taking the five years together, divide total revenue by total quantity exported:

\[ \begin{aligned} \text{revenue} &= 20+15+35+40+50 = 160\ \text{crore} \\ \text{quantity} &= 10+5+15+20+30 = 80\ \text{lakh} \\ \text{per unit} &= \tfrac{160}{80} \times 100 = \text{Rs. } 200 \end{aligned} \]

Averaging the five yearly figures instead (200, 300, 233, 200 and 167) would give about Rs. 220, which is not among the options, so the key uses the overall ratio. Rs. 166, Rs. 233 and Rs. 300 are the single-year figures for 2015, 2013 and 2012.

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Direction for [ Question No: 9 To 10 ] :

Direction : The following questions are based on the following pie-diagram :

(The pie-diagram is given here as a table of its labelled shares.)

Sector	Share
A : Printing cost	35%
B : Cost of paper	20%
C : Royalty	15%
D : Advertisement charges	20%
E : Other charges	x%

If the cost of paper is Rs. 16,000, then find the amount of other charges :

A.Rs. 16,000
B.Rs. 10,000
C.Rs. 8,000
D.Rs. 12,000

Exam Year(s)

MH SET - 2019, SET Exam - 2019,

Answer: C

The other charges amount to Rs. 8,000.

The shares must total 100%, so other charges are \(x = 100 - (35 + 20 + 15 + 20) = 10\%\). Paper is 20% and costs Rs. 16,000:

\[ \begin{aligned} \text{total} &= 16000 \div 0.20 = 80000 \\ \text{other} &= 10\% \times 80000 = 8000 \end{aligned} \]

Rs. 16,000 assumes other charges equal paper, and Rs. 12,000 is the royalty (15%), not the other charges.

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10.

The tax deducted at source is 10% of the royalty amount then the amount of tax paid is ............... .

A.Rs. 1,200
B.Rs. 800
C.Rs. 1,000
D.Rs. 8,000

Exam Year(s)

MH SET - 2019, SET Exam - 2019,

Answer: A

The tax paid is Rs. 1,200.

From the same pie-diagram, the total cost is Rs. 80,000 (paper, 20%, is Rs. 16,000), and royalty is 15% of it.

\[ \begin{aligned} \text{royalty} &= 15\% \times 80000 = 12000 \\ \text{TDS} &= 10\% \times 12000 = 1200 \end{aligned} \]

Rs. 800 is 10% of the other charges, Rs. 1,000 is a rounded guess, and Rs. 8,000 is the other charges themselves.

Interpretation of Data Questions and Answers

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Interpretation of Data Questions and Answers

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