Data Interpretation Questions and Answers

Answer: A

The share in Grade III is 22.7 per cent.

Grade III holds 7% of the universities and 23% of the colleges, so count the institutions in each and divide by the total of 504 + 25951 = 26455.

\[ \begin{aligned} 0.07 \times 504 &= 35.28 \\ 0.23 \times 25951 &= 5968.73 \\ 35.28 + 5968.73 &= 6004.01 \end{aligned} \]

\[ \frac{6004.01}{26455} \times 100 \approx 22.7\% \]

Because colleges outnumber universities about fifty to one, the result sits just below the college figure of 23%. Taking the plain average of 7% and 23% gives 15.0, which wrongly gives both groups equal weight; 23.7 and 66.8 do not come from the Grade III shares at all.

Answer: C

The true statement is that VK's yearly batting average is consistently higher than that of RS between the two world cup years.

Between 2015 and 2019 lie 2016, 2017 and 2018. In each, VK's bar is above RS's: about 92 against 63, 77 against 72, and 133 against 74.

The other statements fail on one year each. RS is not higher in every world cup year, because in 2019 VK (about 60) is slightly above RS (about 58). VK is not higher in every world cup year, because in 2015 RS (about 51) is well above VK (about 37). And RS is not consistently higher in the last three years, because in 2021 VK (about 43) is above RS (about 30).

Answer: C

The true statement is that VK's yearly batting average is consistently higher than that of RS between the two world cup years.

Between 2015 and 2019 lie 2016, 2017 and 2018. In each, VK's bar is taller: about 92 against 62, 77 against 72, and 133 against 74.

The others fail on the chart. In 2015 RS (about 51) is above VK (about 36), so VK is not higher in every world cup year; in 2019 VK (about 60) is just above RS (about 57), so RS is not higher in every world cup year either. In the last three years RS is higher in 2020 and 2022 but VK is higher in 2021 (about 43 against 30), so RS is not consistently higher.

Answer: A

The correct chart is V 10%, R 20%, Y 30%, G 40%.

Write the four statements as equations: \(Y + 2V = 50\), \(V + G = 50\), \(Y + R = 50\) and \(V + 2R = 50\). The first and last both equal 50, so

\[ \begin{aligned} Y + 2V &= V + 2R \Rightarrow Y + V = 2R \\ (50 - R) + V &= 2R \Rightarrow V = 3R - 50 \\ (3R - 50) + 2R &= 50 \Rightarrow R = 20 \end{aligned} \]

Then \(V = 10\), \(Y = 50 - 20 = 30\) and \(G = 50 - 10 = 40\). The total is 100 balls, so the counts are also the percentages: V 10%, R 20%, Y 30%, G 40%.

The other charts fail a statement at once. V 40% would make \(Y + 2V\) at least 80, not 50; V 30% with Y 10% gives \(10 + 60 = 70\); V 20% with Y 40% gives \(40 + 40 = 80\).

Answer: A

The total capacity is 12500 kg.

In 2005, supply was 60% of demand and demand was 80% of capacity. Work back from the supply.

\[ \begin{aligned} \text{demand} &= \frac{6000}{0.60} = 10000 \\ \text{capacity} &= \frac{10000}{0.80} = 12500 \end{aligned} \]

10000 is the demand, the trap for anyone who stops after the first step. 16500 does not follow from the 2005 values. In one line, capacity is supply divided by both percentages: \(6000 \div (0.6 \times 0.8) = 12500\).

Answer: B

The approximate average supply in the key is 5375 kg.

With capacity fixed at 10000 kg, each year's supply is capacity times the demand share times the supply share.

\[ \begin{aligned} 2003 &: 10000 \times 0.80 \times 0.65 = 5200 \\ 2004 &: 10000 \times 0.90 \times 0.70 = 6300 \\ 2005 &: 10000 \times 0.80 \times 0.60 = 4800 \\ 2006 &: 10000 \times 0.65 \times 0.90 = 5850 \end{aligned} \]

\[ \text{average} = \frac{22150}{4} = 5537.5 \]

The exact average, 5537.5 kg, is not among the options. The question asks for an approximate value, and 5375 is the closest option to it (about 160 kg away), so the key takes 5375. 6200 is more than 650 kg away, and 5100 and 4400 are further still.

Answer: C

The capacity is highest in 2005.

Supply = capacity × (demand share) × (supply share). If supply is the same every year, capacity is largest where the product of the two shares is smallest.

\[ \begin{aligned} 2003 &: 0.80 \times 0.65 = 0.520 \\ 2004 &: 0.90 \times 0.70 = 0.630 \\ 2005 &: 0.80 \times 0.60 = 0.480 \\ 2006 &: 0.65 \times 0.90 = 0.585 \end{aligned} \]

2005 has the smallest product, 0.48, so the same supply needs the largest capacity behind it. 2004 is the opposite case, with the smallest capacity. 2006 is the trap: its supply share is the highest of all, but its low demand share pulls the product up to 0.585.

Answer: C

Actual profit exceeds estimated profit in 2 years.

\[ \begin{aligned} \text{Est.} &: 295,\ 401,\ 204 \\ \text{Actual} &: 338,\ 210,\ 384 \end{aligned} \]

Each figure is revenue minus cost for 2007, 2008 and 2009. For example, the 2007 estimate is \(1281 - 986 = 295\) and the 2007 actual is \(1326 - 988 = 338\).

Actual profit is higher in 2007 (338 against 295) and in 2009 (384 against 204), but lower in 2008 (210 against 401), because actual sales in 2008 fell short of the estimate while costs ran over. So the count is two, not one or three.

Answer: C

The best forecasting year is 2009.

The measure is estimated sales divided by actual sales, and the question defines the lower value as the better forecast.

\[ \begin{aligned} 2007 &: 1281 \div 1326 \approx 0.966 \\ 2008 &: 1452 \div 1286 \approx 1.129 \\ 2009 &: 1228 \div 1452 \approx 0.846 \end{aligned} \]

2009 gives the lowest ratio, 0.846. 2008 is the worst by this rule, since the estimate exceeded actual sales. 2007 has the ratio closest to 1, which would be the most accurate forecast in ordinary terms, but the question's own rule says lower is better, so the data are enough and 'Cannot be determined' is wrong.

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.