Data Interpretation Questions and Answers

Answer: C

The percentage is 25%.

Use the diagram for the 60 candidates who cleared E₂ in the first stage. Those who cleared the viva are 30 (cleared both) + 15 (cleared viva but failed E₁) = 45.

\[ \begin{aligned} \text{failed viva} &= 60 - 45 = 15 \\ \text{percentage} &= \frac{15}{60} \times 100 = 25\% \end{aligned} \]

The 15 who failed are the 10 who cleared E₁ but failed the viva and the 5 who failed both.

75% is the share who passed the viva. 66·7% is 40/60, the share who cleared E₁, and 33·3% is 15/45, which compares the failures with those who passed instead of with all 60.

Answer: C

C has the greatest BMI.

BMI is mass divided by the square of height:

\[ \begin{aligned} A &: 45 / 1.45^2 \approx 21.4 \\ B &: 50 / 1.50^2 \approx 22.2 \\ C &: 55 / 1.55^2 \approx 22.9 \\ D &: 60 / 1.70^2 \approx 20.8 \end{aligned} \]

E, not offered, gives \(70 / 1.80^2 \approx 21.6\).

The trap is to pick the heaviest person: D weighs more than C, but D's greater height, squared, more than cancels the extra weight. B is second, and A has the lowest weight but not the lowest BMI.

Answer: D

The distance cannot be determined.

The bar chart gives each city's distance from New Delhi only: Ranchi 1,000 km and Munnar 2,000 km. Nothing in the chart or the information list says in which direction each city lies from New Delhi, or the angle between the two routes.

Two distances from a common point fix a third distance only when the directions are known. 3,000 km would hold only if the two cities lay on opposite sides of New Delhi on one straight line, and 2,000 km is just Munnar's distance from New Delhi. 800 km does not follow from the data either.

Answer: B

Both trips would take the same amount of time.

The chart puts Kolkata and Pune at the same distance from New Delhi, 1,200 km. A plane to Kolkata pushes against the easterly wind on the way out and is carried by it on the way back. A plane to Pune is carried by the wind on the way out and pushes against it on the way back.

So each round trip is 2,400 km with one leg into the 2 km/hour wind and one leg with it, at the same constant speed. The two trips are identical in every factor that affects time.

Choosing either city alone looks at only one leg of its round trip. 'Cannot be determined' is wrong because the distances and the wind effect are both given.

Answer: B

The fewest temporary employees were employed in 2014.

In the stacked bar chart, the temporary workers are the white upper part of each bar, from the top of the black (permanent) part to the top of the bar. Reading the bars: in 2013 the bar rises from about 325 to about 525 (about 200 temporary), in 2014 from about 350 to about 525 (about 175), in 2016 from about 400 to about 645 (about 245), and in 2018 from about 450 to about 650 (about 200).

2014's white segment is the shortest, about 175 workers. 2013 and 2018 have about 200 each, and 2016 about 245, so those options are wrong.

Answer: C

The permanent workers' share of workhours was lowest in 2015.

The permanent workers' share is 10P / (10P + 6T), with P and T read from the chart:

\[ \begin{aligned} 2013 &: 3250/4450 \approx 73\% \\ 2014 &: 3500/4550 \approx 77\% \\ 2015 &: 3750/5850 \approx 64\% \\ 2016 &: 4000/5470 \approx 73\% \end{aligned} \]

2015 stands out because it had by far the most temporary workers, about 350, nearly as many as its 375 permanent workers, so the temporary workers' hours took a much larger share that year than in 2013, 2014 or 2016.

Answer: C

Women aged 25 - 34 make up 50 per cent.

The pie chart gives 450 women aged 20 - 24, 350 aged 25 - 29, 150 aged 30 - 34 and 50 aged 35 - 40, a total of 1000.

\[ \begin{aligned} 350 + 150 &= 500 \\ 500 / 1000 &= 50\% \end{aligned} \]

35 is the share of the 25 - 29 group alone, and 15 the share of the 30 - 34 group alone. 80 adds the 20 - 24 group to the 25 - 29 group instead of the two groups asked about.

Answer: D

The number aged 27 or above is 325.

The 25 - 34 group has 350 + 150 = 500 women, and 25% of them, 125, are aged 27 - 29. Women aged 27 or above are those aged 27 - 29, plus everyone in the 30 - 34 and 35 - 40 groups:

\[ 125 + 150 + 50 = 325 \]

550 counts the whole of the 25 - 34 group plus the 35 - 40 group, instead of only those aged 27 and above. 200 counts only the women aged 30 and above and leaves out the 27 - 29 group. 425 does not match any correct grouping of the ages.

Answer: A

The percentage aged 31 or above is 11.

Of the 150 women aged 30 - 34, 60% (90 women) were 30, so 60 were aged 31 - 34. Adding the 50 women aged 35 - 40:

\[ \begin{aligned} 60 + 50 &= 110 \\ 110 / 1000 &= 11\% \end{aligned} \]

14 counts the 90 women aged exactly 30 with the 35 - 40 group, the opposite of what is asked. 20 takes the whole 30 - 34 group plus the 35 - 40 group. 13.5 does not correspond to the data.

Answer: C

The percentage having their first child was 61.6.

Apply each group's percentage to the number of women in it and add:

\[ \begin{aligned} 0.80 \times 450 &= 360 \\ 0.60 \times 350 &= 210 \\ 0.30 \times 150 &= 45 \\ 0.02 \times 50 &= 1 \end{aligned} \]

That is 616 first-time mothers out of 1000 women, or 61.6%.

43 is the simple average of the four percentages, (80 + 60 + 30 + 2)/4, which ignores that the groups differ greatly in size. 52.9 and 65.8 do not match the weighted total of 616.