Interpretation of Data Questions and Answers

Answer: D

The employee with the most working days is E.

Add each column over the five years:

• A: 280 + 300 + 310 + 315 + 295 = 1500
• B: 310 + 290 + 300 + 310 + 300 = 1510
• C: 315 + 310 + 315 + 315 + 300 = 1555
• D: 315 + 315 + 310 + 310 + 305 = 1555
• E: 320 + 325 + 320 + 330 + 310 = 1605

E has the highest total, 1605. E also has the highest figure in every single year, which confirms the result without the full addition.

Answer: B

The employees with equal totals are C and D.

The five-year totals are A 1500, B 1510, C 1555, D 1555 and E 1605. Only C and D are equal, at 1555 each.

A and B differ by 10 (1500 against 1510), B and D by 45, and A, B and C are all different. So every option other than 'C and D' names employees whose totals do not match.

Answer: D

8 villages were visited by both salesmen.

Two of the 20 villages were visited by neither, so 18 were visited by at least one. By the inclusion-exclusion principle:

\[ \begin{aligned} n(A \cup B) &= n(A) + n(B) - n(A \cap B) \\ 18 &= 14 + 12 - n(A \cap B) \\ n(A \cap B) &= 8 \end{aligned} \]

The option 26 simply adds 14 and 12, counting the shared villages twice; 6 is the number visited by A alone (14 - 8), and 4 the number visited by B alone (12 - 8).

Answer: B

18 villages were visited by at least one salesman.

There are 20 villages, and 2 of them were visited by neither salesman. Every other village was visited by A, by B or by both, so the number visited by at least one is 20 - 2 = 18.

As a check: 14 + 12 - 8 = 18, using the 8 villages both of them visited. The option 26 is 14 + 12, which counts those 8 twice, and 20 forgets the 2 villages that neither visited.

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.