Data Interpretation Questions and Answers

Answer: C

The maximum possible profit is 428.

For each year, take the larger of the estimated and actual revenue and subtract the smaller of the estimated and actual cost.

\[ \begin{aligned} 2007 &: 1326 - 986 = 340 \\ 2008 &: 1452 - 1051 = 401 \\ 2009 &: 1452 - 1024 = 428 \end{aligned} \]

The largest of the three is 428, in 2009, where the actual revenue (1452) was the higher figure and the estimated cost (1024) the lower. 340 and 401 are the values for 2007 and 2008, which catch anyone who stops at the first or second year.

Answer: C

About 38800 asylum seekers applied to countries outside the table.

In 2010 the USA's 72800 applications were 15% of all applications, which gives the total.

\[ \begin{aligned} \text{total} &= \frac{72800}{0.15} \approx 485333 \\ \text{table, 2010} &= 92\% \\ \text{others} &= 8\% \times 485333 \approx 38827 \end{aligned} \]

The 92% is the sum of the fifteen countries' 2010 column (15 + 13 + 11 + 3 + 9 + 6 + 6 + 6 + 4 + 3 + 3 + 4 + 3 + 3 + 3). The remaining 8% is about 38827, which rounds to 38800. 36400 would be 7.5% of the total, and 37800 and 40200 match no share that the table supports.

Answer: C

The number of students fell in Agriculture.

The bar chart gives about 35000 students in 2001 and 40000 in 2002. Multiply each year's total by the faculty's share.

\[ \begin{aligned} \text{Agri. 2001} &= 8\% \times 35000 = 2800 \\ \text{Agri. 2002} &= 5\% \times 40000 = 2000 \end{aligned} \]

Agriculture fell by 800 students. The other two named faculties grew: Commerce went from \(24\% \times 35000 = 8400\) to \(24\% \times 40000 = 9600\), and Pharmacy from 2450 to 3600. 'None' is wrong because a falling share can mean a falling number even when the total rises, as it does for Agriculture.

Answer: B

Item A accounts for 50/3 % of the expenditure, that is \(16\tfrac{2}{3}\)%.

The angles in a pie chart add to 360°.

\[ \begin{aligned} A &= 360 - (65 + 45 + 90 + 100) = 60^\circ \\ \frac{60}{360} \times 100 &= \frac{50}{3}\% \end{aligned} \]

25 is what you get by dividing 60 by 240 instead of 360, and 175/6 and 25/18 do not correspond to 60° of a 360° circle. A sixth of the circle is always \(16\tfrac{2}{3}\)%, a value worth remembering.

Answer: B

Only two pairs are correctly matched.

Convert each angle to a share of 360°.

\[ \begin{aligned} \text{Food} &= \tfrac{108}{360} \times 100 = 30\% \\ \text{Education} &= \tfrac{54}{360} \times 100 = 15\% \end{aligned} \]

Pair 1 (30%) is right. Pair 2 is right: 108 : 54 = 2 : 1. Pair 3 is wrong: the remaining sectors are \(100 - 30 - 15 = 55\%\), not 60%. 60% would need Education to be 10%, that is 36°, not 54°.

Answer: A

The information is correct in only one row.

Reading the bars: Withdrew 8, F 4, D 8, C 6, B 19 and A 3.

• Row 1 gives grade A as 4; the bar is 3 (4 is the F bar). Wrong.
• Row 2: withdrew 8, grade D 8, grade A 3. All correct.
• Row 3 gives grade C as 8; the bar is 6. Wrong.

So only row 2 is fully correct. Each wrong row changes one value, which is why every entry, not just the first, has to be checked.

Answer: A

The team won 58% of its matches.

Add the matches won and the total played across the seven tournaments:

\[ \begin{aligned} \text{won} &= 5+4+5+6+4+3+2 = 29 \\ \text{played} &= 8+8+7+9+6+6+6 = 50 \end{aligned} \]

\(29/50 = 58\%\). Averaging the seven separate win percentages would give a slightly different figure, because the tournaments have different numbers of matches. 52%, 75% and 80% do not match the totals.

Answer: A

The central angle is 202.5°.

The chart totals \(20 + 100 + 80 + 120 = 320\) office goers. The four-wheelers are cars and buses, \(100 + 80 = 180\) people.

\[ \begin{aligned} \text{angle} &= \frac{180}{320} \times 360^\circ \\ &= 202.5^\circ \end{aligned} \]

Counting only cars would give \(\frac{100}{320} \times 360^\circ = 112.5^\circ\), which is not an option, a sign that buses belong in the four-wheeler group. 203° to 204° are rounding traps around the exact value.

Answer: B

The salary fell by 25%.

Reading the graph, Deepak's salary was 20 thousand in 2010 and 15 thousand in 2013, a fall of 5 thousand.

\[ \begin{aligned} \text{decrease} &= \frac{20 - 15}{20} \times 100 \\ &= 25\% \end{aligned} \]

The base of a percentage change is the earlier value, 2010's 20 thousand.

33.33% is what you get by dividing the fall by the 2013 value, 15, instead of 20. 20% would be the fall from 2011 to 2012 (25 to 20). 'None of these' is wrong because 25% is offered.

Answer: D

The angle of part B is about 109°.

The whole circle, 360°, represents the total of the three parts, 62 + 31 + 9 = 102. Part B's share is

\[ \begin{aligned} \theta_{B} &= \frac{31}{102} \times 360^{\circ} \\ &\approx 109.4^{\circ} \approx 109^{\circ} \end{aligned} \]

111.6° (option B, about 111°) would come from treating the values as percentages of 100, which they are not, since they total 102. 108° and 113° do not match the share either.