Interpretation of Data Questions and Answers

Answer: C

The labour sector has an angle of 90°.

In a pie diagram the whole, 100 per cent, is the full circle of 360°, so each per cent is 3.6°.

\[ 25 \times 3.6^{\circ} = 90^{\circ} \]

25° copies the percentage without converting it, and 30° and 50° do not correspond to 25 per cent of the circle.

Answer: D

The ratio is 3 : 10.

Cement and bricks account for 30 per cent of the total expenditure, that is 30 out of 100.

\[ 30 : 100 = 3 : 10 \]

1 : 3 would be about 33 per cent and 1 : 4 is 25 per cent, which is labour's share; 2 : 5 would be 40 per cent.

Answer: B

Agra's share is 25.00%.

The total for all places is 15.0 + 20.0 + 10.0 + 6.0 + 6.0 + 3.0 = 60.0 lakh tourists, of whom 15.0 lakh visited Agra.

\[ \frac{15}{60} \times 100 = 25\% \]

33.33% is Delhi's share (20 of 60), 16.67% is Chennai's (10 of 60), and 10.00% is Udaipur's or Bangalore's (6 of 60).

Answer: B

The largest group at Delhi is English.

Delhi's row shows 8.2 lakh American, 8.7 lakh English, 2.7 lakh French and 0.4 lakh other tourists. English tourists (8.7) are the most numerous, just ahead of Americans (8.2).

Americans are the largest group at most other places in the table, which is the trap; at Delhi the English outnumber them.

Answer: B

The angle for 'other' is 90°.

The angles of a pie chart add up to 360°:

\[ \begin{aligned} x &= 360 - (108 + 63 + 72 + 27) \\ &= 360 - 270 = 90^\circ \end{aligned} \]

63°, 108° and 72° are the angles already given for clothing, food and house rent, not the remaining sector.

Answer: B

Food accounts for 30% of the expenses.

A sector's share of the total is its angle divided by 360°:

\[ \frac{108}{360} \times 100 = 30\% \]

25% would be a 90° sector, the 'other' expenses, and 20% a 72° sector, house rent. 90% confuses the 'other' sector's angle with a percentage.

Answer: A

The difference is maximum for Engineering and allied.

Subtract district B from district E for each type:

\[ \begin{aligned} \text{Agro} &: 165 - 86 = 79 \\ \text{Forest} &: 120 - 70 = 50 \\ \text{Livestock} &: 176 - 90 = 86 \\ \text{Textile} &: 132 - 92 = 40 \\ \text{Chemical} &: 154 - 86 = 68 \\ \text{Engineering} &: 166 - 76 = 90 \end{aligned} \]

The largest difference, 90, is for engineering and allied. Agro-based (79) and chemical-based (68) are smaller, and textile-based has the smallest difference of all.

Answer: B

The percentage is 17.2%.

District B has 86 agro-based companies out of a total of 500:

\[ \frac{86}{500} \times 100 = 17.2\% \]

86% treats the count as a percentage, 8.6% divides by 1000 instead of 500, and 16.67% would be one-sixth, the share if all six types were equal.

Answer: C

61 players play only one game.

Those in exactly two games are the pairwise figures minus the 3 who play all three:

\[ \begin{aligned} \text{two} &= (8-3) + (10-3) + (7-3) = 16 \\ \text{union} &= 102 - (8 + 10 + 7) + 3 = 80 \\ \text{one} &= 80 - 16 - 3 = 61 \end{aligned} \]

The union equals the 80 players, so everyone plays at least one game. 102 is the plain sum 35 + 42 + 25 without removing overlaps, 80 is everyone, and 63 does not match any count that can be formed from the figures given, such as one game (61) or two games (16).

Answer: D

16 players play exactly two games.

Each pairwise figure includes the 3 players who play all three games, so subtract them from each pair:

\[ \begin{aligned} \text{C and H only} &= 8 - 3 = 5 \\ \text{C and F only} &= 10 - 3 = 7 \\ \text{H and F only} &= 7 - 3 = 4 \\ \text{total} &= 5 + 7 + 4 = 16 \end{aligned} \]

19 is that total plus the 3 who play all three games. 61 is the number who play only one game, and 80 is all the players.