Data Interpretation Questions and Answers

Answer: B

The ratio is 3 : 4.

Statement I: the average of 8 boys rises by 2, so their total rises by 16. The two new boys together are 16 years older than the two they replaced:

\[ \begin{aligned} \text{new total} &= 21 + 23 + 16 = 60 \\ x &= 30 \end{aligned} \]

Statement II: three years ago A + B + C = 81, so now it is 90. Five years ago B + C = 40, so now it is 50. Hence \(y = 90 - 50 = 40\).

So \(x : y = 30 : 40 = 3 : 4\).

Answer: C

There are 620 illiterate persons below the poverty line.

40% of males = 8800, so there are 22,000 males. From 11 : 10 : 9 there are 20,000 females and 18,000 children aged 10 and above; children below 10 are 10% of females, 2,000. Total population = 62,000.

\[ \begin{aligned} \text{below poverty line} &= 5\% \times 62000 = 3100 \\ \text{illiterate among them} &= 20\% \times 3100 = 620 \end{aligned} \]

3100 is the whole below-poverty-line group, and 2480 is the literate part of it (80%).

Answer: B

The total population is 62000.

Since 40% of males are 8800, males = 22,000. The ratio 11 : 10 : 9 then gives 20,000 females and 18,000 children aged 10 and above. Children below 10 are 10% of females, 2,000.

\[ 22000 + 20000 + 18000 + 2000 = 62000 \]

60,000 forgets the children below 10 years, the trap in this set; 42,000 and 40,000 leave out other groups.

Children below 10 are counted from the number of females (10% of 20,000), not from the total population.

Answer: A

There are 14400 literate children aged 10 and above.

Children aged 10 and above are \(\frac{9}{11} \times 22000 = 18000\). 20% of them are illiterate, so 80% are literate:

\[ 80\% \times 18000 = 14400 \]

3,600 (not offered) would be the illiterate children; 16,200 takes 90% instead of 80%, and 12,600 takes 70%.

Note that the 2,000 children below 10 years are a separate group and do not enter this count; the question asks only about children aged 10 and above.

Answer: D

Women are about 32.26% of the population.

\[ \frac{20000}{62000} \times 100 = 32.258... \approx 32.26\% \]

The denominator must be the whole population, including the 2,000 children below 10. Leaving them out gives \(\frac{20000}{60000} = 33.33\%\); 32.86 is a near-miss in the decimals.

Shortcut: 20,000 out of 62,000 is \(\frac{10}{31}\), and \(\frac{1}{31} \approx 3.226\%\), so ten times that is about 32.26%.

Answer: D

The answer is None of these.

30% of the 20,000 females are literate, so 70% are illiterate:

\[ 70\% \times 20000 = 14000 \]

14,000 is not among the numbers offered: 20,000 is all the women, 6,000 the literate women, and 14,400 the literate children. So 'None of these' is correct.

A quick check on the whole set: literate women are 6,000 and illiterate 14,000, which together make the 20,000 women found from the 11 : 10 : 9 ratio.

Answer: D

The maximum was in 1995.

Add the four disciplines for each year and divide selected by received:

• 1991: 125 of 11,200, about 1.12%.
• 1993: 184 of 15,990, about 1.15%.
• 1994: 225 of 17,870, about 1.26%.
• 1995: 258 of 20,210, about 1.28%.

(1992 gives 150 of 14,170, about 1.06%.) 1994 comes close, but 1995 is the highest.

A quick screen: 1995 has both the largest number selected and a selection rate just above 1994's, so there is no need to work out 1991 and 1992 exactly once their rates are seen to be near 1.1%.

Answer: B

The lowest percentage is for Arts, 1992.

Compare the four candidates offered:

• Arts 1992: \(\frac{20}{3160} \approx 0.63\%\).
• Arts 1993: \(\frac{24}{3200} = 0.75\%\).
• Others 1994: \(\frac{47}{4440} \approx 1.06\%\).
• Science 1995: \(\frac{120}{7000} \approx 1.71\%\).

Arts in 1992 had a big jump in applications (from 2000 to 3160) while selections actually fell, from 22 to 20, which is why its rate is the lowest in the whole table.

Answer: D

The maximum increase was in Arts, 1992.

Percentage increase over the previous year for each option:

• Arts 1992: \(\frac{3160 - 2000}{2000} = 58\%\).
• Science 1992: \(\frac{5100 - 3700}{3700} \approx 37.8\%\).
• Arts 1994: \(\frac{4000 - 3200}{3200} = 25\%\).
• Arts 1995: \(\frac{5000 - 4000}{4000} = 25\%\).

Science 1992 has the largest absolute rise (1400), but in percentage terms Arts 1992 is far ahead because its base was small.

Answer: C

The highest combined population density is for A1, A4.

Combine each pair by adding the animal percentages and dividing by the sum of the forest-land percentages:

\[ \begin{aligned} A1, A4 &: (19 + 11) / (15 + 8) = 30/23 \approx 1.30 \\ A4, A5 &: 25/22 \approx 1.14 \\ A1, A3 &: 39/37 \approx 1.05 \\ A3, A6 &: 35/40 = 0.875 \end{aligned} \]

A4 (Europe) has the highest single density, 11/8, and A1 (Asia) the next, 19/15, so their pair comes out on top. A3 and A6 both have more forest land than animals, which pulls their pairs below 1.