Interpretation of Data Questions and Answers

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.

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.

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.

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.

Answer: C

State D has 28,000 male employees.

State D has 40,000 employees in the ratio of males to females 14 : 6, so males are 14 parts out of 20:

\[ \frac{14}{20} \times 40000 = 28000 \]

14,000 and 6,000 just read the ratio terms as thousands, and 20,000 is half the total.

Answer: D

State B has 7,000 post-graduate female employees.

State B has 30,000 employees in the ratio 8 : 7, so females are 7 parts out of 15, and 50 percent of employees are post-graduates. Applying that percentage to the female employees:

\[ \begin{aligned} \text{females} &= \tfrac{7}{15} \times 30000 = 14000 \\ \text{PG females} &= 50\% \times 14000 = 7000 \end{aligned} \]

15,000 is the number of all post-graduates in state B, 8,000 is half the male employees (16,000), and 350 is a decimal slip.

Answer: B

The possible maximum is 30.

A student who passed in all four subjects is counted in every one of the four columns for Division B: 34 in English, 32 in Hindi, 36 in Marathi and 30 in History. The number who passed all four can therefore be no larger than the smallest of these counts, the 30 who passed History, and it can equal 30 if every History passer also passed the other three.

34 and 36 are the English and Marathi counts and would require more students to pass all four than passed History. 26 is a possible value but not the maximum.

Answer: A

The maximum possible number is 93.

In each division, the number passing both Hindi and Marathi can be at most the smaller of the two counts. The maximum for the three divisions combined is the sum of these:

\[ \begin{aligned} A &: \min(30, 38) = 30 \\ B &: \min(32, 36) = 32 \\ C &: \min(34, 31) = 31 \\ \text{Total} &= 30 + 32 + 31 = 93 \end{aligned} \]

96 is the total of the Hindi column (30 + 32 + 34), but division C has only 31 Marathi passers, so all 34 Hindi passers there cannot have passed Marathi. 105 is the Marathi total and 111 adds larger figures still, both impossible for the same reason.

Answer: B

A table is used to show exact values.

A table presents data in rows and columns as actual figures, so the reader can see each value exactly and look up precise numbers.

Pie charts, bar diagrams and dot plots are graphical displays. They are good for showing proportions, comparisons and distributions at a glance, but the reader judges values from the size of slices, the height of bars or the position of dots, which gives only approximate values. When exact values matter, a table is the right choice.

Answer: C

The correct statements are (i), (ii) and (iv).

The total number of families is 42 + 40 + 36 + 18 + 5 = 141.

\[ \begin{aligned} \text{(i)}\ \frac{40 + 36}{141} &= \frac{76}{141} \approx 53.9\% \\ \text{(ii)}\ \frac{40 + 36 + 18 + 5}{141} &= \frac{99}{141} \approx 70.2\% \end{aligned} \]

So (i), about 54 per cent between Rs. 10,000 and Rs. 20,000, and (ii), 70 per cent earning more than Rs. 10,000, are both correct. For (iv), the median is the 71st family in order of income; the first band holds 42 families and the first two hold 82, so the 71st falls in the band Rs. 10,000-14,999, and (iv) is correct.

Statement (iii) cannot be known: the table says only that the highest band runs from Rs. 25,000 to Rs. 30,000, not what the richest family earns. Every code containing (iii) is therefore wrong.