Data Interpretation Questions and Answers

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.

Answer: C

The fewest students were placed in Consulting.

Convert each percentage to a number of students using the year's total (800 in 2015, 1000 in 2016, 1200 in 2017):

Consulting has the smallest three-year total, 272. Others comes close at 296, and Operations/Supply chain (382) and Marketing/Sales (424) are well above it.

Answer: B

About 21 per cent were placed in General Management.

General Management took 12% of 800 in 2015, 25% of 1000 in 2016 and 24% of 1200 in 2017:

\[ \begin{aligned} 96 + 250 + 288 &= 634 \\ 800 + 1000 + 1200 &= 3000 \\ 634 / 3000 &\approx 21.1\% \end{aligned} \]

The trap is to average the three percentages directly, (12 + 25 + 24)/3 = 20.3%, which ignores that the years had different numbers of students. 24 and 26 are too high, and 19 too low.

Answer: D

Placements rose in 4 sectors.

Compare the actual numbers, 2015 (out of 800) against 2017 (out of 1200):

Systems/IT, General Management, Operations/Supply chain and Marketing/Sales increased; Consulting and Others fell. Operations is the case to watch: its share fell from 20% to 16%, yet the number rose because the total grew from 800 to 1200, so counting by percentages alone gives 3, a wrong answer.

Answer: A

The total placed in Marketing/Sales was 424.

Marketing/Sales took 11% of 800 in 2015, 18% of 1000 in 2016 and 13% of 1200 in 2017:

\[ \begin{aligned} 0.11 \times 800 &= 88 \\ 0.18 \times 1000 &= 180 \\ 0.13 \times 1200 &= 156 \\ 88 + 180 + 156 &= 424 \end{aligned} \]

524 is exactly 100 too many, and 400 and 350 are too few; none of them equals the sum of the three years' placements.

Answer: D

The top three countries never out-weigh the rest, so the answer is None of these: it happens in 0 years.

Add up each year's column and take the three largest shares:

\[ \begin{aligned} 2007 &: \text{all } 86,\ \text{top three } 15 + 11 + 9 = 35 \\ 2008 &: \text{all } 87,\ \text{top three } 13 + 10 + 9 = 32 \\ 2009 &: \text{all } 89,\ \text{top three } 13 + 11 + 9 = 33 \\ 2010 &: \text{all } 92,\ \text{top three } 15 + 13 + 11 = 39 \\ 2011 &: \text{all } 93,\ \text{top three } 17 + 12 + 10 = 39 \end{aligned} \]

The remaining twelve countries hold 51, 55, 56, 53 and 54, which is more than the top three every year. So the number of years is zero, which is not offered as 1, 2 or 3.

Answer: C

The ranks of Germany add up to 24.

Rank each year by share, counting tied countries at the same rank and skipping the next rank, as the key does:

\[ \begin{aligned} 2007 &: \text{share } 6,\ \text{rank } 7 \\ 2008 &: \text{share } 6,\ \text{rank } 6 \\ 2009 &: \text{share } 7,\ \text{rank } 5 \\ 2010 &: \text{share } 11,\ \text{rank } 3 \\ 2011 &: \text{share } 10,\ \text{rank } 3 \end{aligned} \]

In 2007 six countries are above Germany (USA 15, Sweden 11, France 9, and UK, Canada and Greece at 8), so Germany is 7th. In 2008 five are above it (13, 10, 9, 8, 8) and Sweden ties with it at 6. In 2009 four are above (13, 11, 9, 8), and in 2010 and 2011 only the USA and France are above. The sum is 7 + 6 + 5 + 3 + 3 = 24. Ranking without skipping after ties would give 21, which is not offered.

Answer: D

The figure cannot be determined.

Each percentage in the table is a share of that year's total number of applications, and the yearly totals are not given. USA's five shares add up to 73, but the 278800 applications are the sum of 15%, 13%, 13%, 15% and 17% of five different totals. Without the yearly totals, France's 54 (the sum of its shares) cannot be turned into a number of applications.

If the totals were assumed equal, France would get \(\frac{54}{73} \times 278800 \approx 206000\), which matches none of the figures offered, so 216000, 262800 and 243900 are not obtainable by any reading.

Answer: A

The USA shows the minimum variation: none, since it is first in both years.

Rank the four countries in 2007 and 2011 by share, with tied countries on the same rank:

\[ \begin{aligned} \text{USA} &: 1 \to 1,\ \text{change } 0 \\ \text{France} &: 3 \to 2,\ \text{change } 1 \\ \text{Germany} &: 7 \to 3,\ \text{change } 4 \\ \text{UK} &: 4 \to 6,\ \text{change } 2 \end{aligned} \]

In 2007 the UK's 8% is tied with Canada and Greece behind USA, Sweden and France, and in 2011 its 6% is tied with Belgium and Canada behind five countries. The smallest change is the USA's zero.