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Cyprus Public Service Scales A7-A9 study materials
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Cyprus Public Service Scales A7-A9 practice questions

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Question 1Numerical reasoning

A government department's budget was €250,000. If the budget is increased by 12%, what is the new budget?

  1. €262,000
  2. €275,000
  3. €280,000 Correct answer.
  4. €290,000

Explanation

To find the new budget, calculate the increase: 12% of €250,000 = 0.12 * 250,000 = €30,000. Add the increase to the original budget: €250,000 + €30,000 = €280,000. Alternatively, multiply directly by 1.12: 250,000 * 1.12 = €280,000.

Question 2Numerical reasoning

A project team of 8 officers can complete a data entry task in 6 days. If the team is expanded to 12 officers, how many days will it take to complete the same task, assuming all officers work at the same rate?

  1. 3 days
  2. 4 days Correct answer.
  3. 5 days
  4. 9 days

Explanation

This is an inverse proportion problem. The total work in officer-days is 8 officers * 6 days = 48 officer-days. With 12 officers, the time required is 48 officer-days / 12 officers = 4 days.

Question 3Numerical reasoning

A ministry splits a development grant of €120,000 between three local programs in the ratio 2:3:5. How much does the program with the largest share receive?

  1. €24,000
  2. €36,000
  3. €60,000 Correct answer.
  4. €72,000

Explanation

First, find the total parts: 2 + 3 + 5 = 10 parts. Value of one part: €120,000 / 10 = €12,000. The largest share is 5 parts: 5 * €12,000 = €60,000.

Question 4Numerical reasoning

If a vehicle travels at a constant speed of 75 km/h, how far will it travel in 2 hours and 20 minutes?

  1. 150 km
  2. 165 km
  3. 175 km Correct answer.
  4. 180 km

Explanation

Convert the time to hours: 2 hours and 20 minutes = 2 + 20/60 = 2 + 1/3 = 7/3 hours. Distance = Speed * Time = 75 km/h * (7/3) hours = 25 * 7 = 175 km.

Question 5Numerical reasoning

An office bought 15 laptops and 10 printers for a total cost of €17,500. If the average cost of a printer is €250, what is the average cost of a laptop?

  1. €900
  2. €1,000 Correct answer.
  3. €1,100
  4. €1,200

Explanation

Total cost of printers = 10 * €250 = €2,500. Total cost of laptops = €17,500 - €2,500 = €15,000. Average cost of a laptop = €15,000 / 15 = €1,000.

Question 6Numerical reasoning

A department has 60 employees. If 45% of the employees are female, how many male employees work in the department?

  1. 27
  2. 30
  3. 33 Correct answer.
  4. 36

Explanation

If 45% are female, then 100% - 45% = 55% are male. Number of male employees = 55% of 60 = 0.55 * 60 = 33 employees. (Alternatively, female employees = 0.45 * 60 = 27; males = 60 - 27 = 33).

Question 7Numerical reasoning

If the ratio of successful candidates to unsuccessful candidates in an exam is 3:7, and 150 candidates passed, what was the total number of candidates who took the exam?

  1. 350
  2. 450
  3. 500 Correct answer.
  4. 700

Explanation

The ratio is 3 successful parts to 7 unsuccessful parts, making the total parts 3 + 7 = 10. The successful candidates represent 3 parts: 3 parts = 150, so 1 part = 150 / 3 = 50. Total candidates = 10 parts * 50 = 500.

Question 8Numerical reasoning

A government building consumes 4,200 kWh of electricity in 30 days. Assuming constant daily consumption, how much electricity will it consume in 45 days?

  1. 5,600 kWh
  2. 6,300 kWh Correct answer.
  3. 7,200 kWh
  4. 8,400 kWh

Explanation

Daily consumption = 4,200 kWh / 30 days = 140 kWh/day. Consumption in 45 days = 140 kWh/day * 45 days = 6,300 kWh.

Question 9Numerical reasoning

The average score of 5 candidates in a public service interview is 78. If a 6th candidate is added and the average score rises to 80, what score did the 6th candidate receive?

  1. 82
  2. 85
  3. 90 Correct answer.
  4. 92

Explanation

Sum of scores of 5 candidates = 5 * 78 = 390. Sum of scores of 6 candidates = 6 * 80 = 480. Score of the 6th candidate = 480 - 390 = 90.

Question 10Numerical reasoning

A public sector supplier offers a 15% discount on an invoice of €8,400 if paid within 10 days. What is the discounted amount to be paid?

  1. €1,260
  2. €6,800
  3. €7,140 Correct answer.
  4. €7,560

Explanation

Calculate the discount: 15% of €8,400 = 0.15 * 8,400 = €1,260. The amount to be paid is the original amount minus the discount: €8,400 - €1,260 = €7,140. (Alternatively, calculate 85% of €8,400: 8,400 * 0.85 = €7,140).

Question 11Numerical reasoning

In a department, the ratio of administrative officers to technical officers is 3:5. If 12 technical officers resign, the ratio becomes 3:4. How many administrative officers work in the department?

  1. 36 Correct answer.
  2. 48
  3. 60
  4. 72

Explanation

Let the number of administrative officers be 3x and technical officers be 5x. After 12 technical officers resign, their number becomes 5x - 12. The new ratio is 3x / (5x - 12) = 3/4. Solve for x: 12x = 15x - 36 => 3x = 36 => x = 12. The number of administrative officers is 3x = 3 * 12 = 36.

Question 12Numerical reasoning

An administrative office spends 40% of its budget on salaries, 25% on rent, 15% on utilities, and the remaining €30,000 on office supplies. What is the total budget of the office?

  1. €100,000
  2. €120,000
  3. €150,000 Correct answer.
  4. €200,000

Explanation

The percentage spent on salaries, rent, and utilities is 40% + 25% + 15% = 80%. The remaining budget for supplies is 100% - 80% = 20%. Let B be the total budget: 20% of B = €30,000 => 0.2B = 30,000 => B = 30,000 / 0.2 = €150,000.

Question 13Numerical reasoning

A town's population was 12,000. It increased by 10% in the first year and then decreased by 5% in the second year. What is the population at the end of the second year?

  1. 12,500
  2. 12,540 Correct answer.
  3. 12,600
  4. 13,200

Explanation

Population after year 1: 12,000 * 1.10 = 13,200. Population after year 2: 13,200 * (1 - 0.05) = 13,200 * 0.95 = 12,540.

Question 14Numerical reasoning

A team of 15 programmers can complete a software project in 40 days. If the project must be completed in 25 days, how many additional programmers must be hired, assuming all work at the same rate?

  1. 9 Correct answer.
  2. 12
  3. 15
  4. 24

Explanation

Total work = 15 programmers * 40 days = 600 programmer-days. To complete in 25 days, the number of programmers needed is 600 programmer-days / 25 days = 24 programmers. The number of additional programmers to hire is 24 - 15 = 9 programmers.

Question 15Numerical reasoning

Consider the following data table representing the quarterly tax revenue of a municipality (in thousands of Euros): Q1: €450 Q2: €520 Q3: €480 Q4: €550 What is the percentage increase in tax revenue from Q1 to Q4?

  1. 18.2%
  2. 20.0%
  3. 22.2% Correct answer.
  4. 25.0%

Explanation

Revenue in Q1 = €450. Revenue in Q4 = €550. Increase = €550 - €450 = €100. Percentage increase = (Increase / Q1 Revenue) * 100 = (100 / 450) * 100 = 22.22%.

Question 16Numerical reasoning

A government bond pays 4% simple interest per year. If an investor purchases a bond for €15,000, what is the total value of the investment (principal + interest) after 6 years?

  1. €18,000
  2. €18,600 Correct answer.
  3. €19,000
  4. €19,600

Explanation

Simple interest = Principal * Rate * Time = 15,000 * 0.04 * 6 = €3,600. Total value = Principal + Interest = €15,000 + €3,600 = €18,600.

Question 17Numerical reasoning

An average of 120 files are processed daily by a department. If the morning shift processes 60% of the files and the afternoon shift processes the rest, how many more files does the morning shift process compared to the afternoon shift?

  1. 24 Correct answer.
  2. 48
  3. 72
  4. 96

Explanation

Morning shift files = 60% of 120 = 72 files. Afternoon shift files = 100% - 60% = 40% of 120 = 48 files. Difference = 72 - 48 = 24 files. (Alternatively, the difference is 60% - 40% = 20% of 120 = 24 files).

Question 18Numerical reasoning

Three administrative assistants can file 150 documents in 2 hours. How many documents can 5 administrative assistants file in 3 hours, assuming all work at the same rate?

  1. 250
  2. 300
  3. 375 Correct answer.
  4. 450

Explanation

Find the filing rate per assistant per hour: 150 documents / (3 assistants * 2 hours) = 150 / 6 = 25 documents per assistant-hour. For 5 assistants working for 3 hours: 5 assistants * 3 hours = 15 assistant-hours. Documents filed = 15 assistant-hours * 25 documents/assistant-hour = 375 documents.

Question 19Numerical reasoning

A municipality increases its waste management fee by 8% in 2024, and then by another 5% in 2025. What is the cumulative percentage increase over these two years?

  1. 13.0%
  2. 13.4% Correct answer.
  3. 13.8%
  4. 14.2%

Explanation

Let the initial fee be 100. Fee after 2024 = 100 * 1.08 = 108. Fee after 2025 = 108 * 1.05 = 113.4. Cumulative percentage increase = ((113.4 - 100) / 100) * 100 = 13.4%.

Question 20Numerical reasoning

Solve for x in the equation: 3(x - 4) + 2(2x + 1) = 32

  1. x = 4
  2. x = 5
  3. x = 6 Correct answer.
  4. x = 7

Explanation

Expand the terms: 3x - 12 + 4x + 2 = 32. Combine like terms: 7x - 10 = 32. Add 10 to both sides: 7x = 42. Divide by 7: x = 6.

Question 21Numerical reasoning

A container holds a mixture of 24 liters of water and 6 liters of pure alcohol. If 10 liters of water are added to the mixture, what is the new percentage of alcohol in the mixture?

  1. 12%
  2. 15% Correct answer.
  3. 18%
  4. 20%

Explanation

Original volume = 24 + 6 = 30 liters. Alcohol volume = 6 liters. After adding 10 liters of water, new total volume = 30 + 10 = 40 liters. New percentage of alcohol = (6 liters / 40 liters) * 100 = 15%.

Question 22Numerical reasoning

An officer's monthly salary of €2,100 is split such that 30% goes to rent, 20% to food, 15% to savings, and the remaining portion to miscellaneous expenses. How much money does the officer spend on miscellaneous expenses monthly?

  1. €630
  2. €735 Correct answer.
  3. €840
  4. €945

Explanation

The percentage allocated to rent, food, and savings is 30% + 20% + 15% = 65%. The remaining percentage for miscellaneous expenses is 100% - 65% = 35%. Monthly miscellaneous expenditure = 35% of €2,100 = 0.35 * 2,100 = €735.

Question 23Numerical reasoning

A legal library has 300 books. If 40% are public law books, and 25% of the public law books are administrative law books, how many administrative law books are in the library?

  1. 30 Correct answer.
  2. 45
  3. 60
  4. 75

Explanation

First, find the number of public law books: 40% of 300 = 0.40 * 300 = 120 books. Next, find the number of administrative law books: 25% of 120 = 0.25 * 120 = 30 books. (Alternatively, 0.40 * 0.25 = 0.10 => 10% of 300 = 30).

Question 24Numerical reasoning

A car travels from Nicosia to Limassol at an average speed of 80 km/h, and returns at an average speed of 120 km/h. What is the average speed for the entire round trip?

  1. 96 km/h Correct answer.
  2. 100 km/h
  3. 104 km/h
  4. 110 km/h

Explanation

This requires calculating the harmonic mean of the speeds, not the arithmetic mean. Harmonic mean = 2 * S1 * S2 / (S1 + S2) = 2 * 80 * 120 / (80 + 120) = 19,200 / 200 = 96 km/h. Alternatively, assume a distance of 240 km: outbound time = 3 hours, return time = 2 hours. Total distance = 480 km, total time = 5 hours. Average speed = 480 / 5 = 96 km/h.

Question 25Numerical reasoning

A public archives department scans documents and saves them as files. If the number of files scanned doubles every 4 days, and the department has scanned 500 files initially, how many files will be scanned after 16 days?

  1. 2,000
  2. 4,000
  3. 8,000 Correct answer.
  4. 16,000

Explanation

This is exponential growth. The doubling period is 4 days. In 16 days, the number of doublings is 16 / 4 = 4 doublings. The population of files after 4 doublings is: 500 * 2^4 = 500 * 16 = 8,000 files.

Question 26Numerical reasoning

The cost of a public project is split between the state, the district, and the EU in the ratio 3:2:5. If the district contributes €1,500,000, what is the total cost of the project?

  1. €3,000,000
  2. €4,500,000
  3. €6,000,000
  4. €7,500,000 Correct answer.

Explanation

The district contributes 2 parts of the total 10 parts (3 + 2 + 5 = 10). If 2 parts = €1,500,000, then 1 part = €750,000. The total project cost is 10 parts: 10 * €750,000 = €7,500,000.

Question 27Numerical reasoning

An investigator reviews case files. They can complete 5 files in 4 hours. If they must review 45 files in a week, how many hours must they work?

  1. 32 hours
  2. 36 hours Correct answer.
  3. 40 hours
  4. 45 hours

Explanation

The rate is 5 files per 4 hours, which is 1.25 files per hour. To review 45 files, the time required is: 45 files / 1.25 files/hour = 36 hours. (Alternatively, 45 is 9 times 5, so time is 9 * 4 hours = 36 hours).

Question 28Numerical reasoning

A department receives a shipment of computers. If it distributes them to its teams such that each team gets 6 computers, there are 4 computers left over. If instead each team gets 8 computers, all teams get 8 except one team which gets only 4 computers. How many computers are in the shipment?

  1. 24
  2. 28 Correct answer.
  3. 32
  4. 36

Explanation

Let t be the number of teams and C the number of computers. First scenario: C = 6t + 4. Second scenario: every team gets 8 except one that gets only 4, so the shipment is 4 short of giving everyone 8: C = 8t - 4. Equating: 6t + 4 = 8t - 4, so 2t = 8 and t = 4. Then C = 6(4) + 4 = 28. Check: with 8 per team, three teams get 8 (24) and the fourth gets 4, totalling 28.

Question 29Numerical reasoning

A district's waste recycling rate increases annually at a compound rate of 10%. If the current recycling rate is 30%, what will the recycling rate be after 3 years?

  1. 39.0%
  2. 39.9% Correct answer.
  3. 42.0%
  4. 43.2%

Explanation

This is a compound growth problem. Rate after 3 years = Current Rate * (1 + Growth Rate)^3 = 30 * (1.10)^3 = 30 * 1.331 = 39.93%.

Question 30Numerical reasoning

A public administrative team is formed by selecting officers from a pool of 6 seniors and 4 juniors. If a committee of 4 officers must be selected, what is the probability that the committee will contain exactly 2 seniors and 2 juniors?

  1. 3/7 Correct answer.
  2. 3/10
  3. 1/2
  4. 3/5

Explanation

The total number of ways to select 4 officers from 10 (6 seniors + 4 juniors) is 10C4 = (10*9*8*7)/(4*3*2*1) = 210 ways. The number of ways to select exactly 2 seniors from 6 is 6C2 = (6*5)/2 = 15. The number of ways to select exactly 2 juniors from 4 is 4C2 = (4*3)/2 = 6. The number of favorable outcomes is 6C2 * 4C2 = 15 * 6 = 90. Probability = Favorable / Total = 90 / 210 = 9/21 = 3/7.

Question 31Numerical reasoning

A government building construction project was originally estimated to take 120 days with 50 workers. After 30 days of work, 10 workers resign. If the project must still be completed on the original schedule, how many additional workers must be hired to replace the resigned workers and complete the project on time?

  1. 0
  2. 10 Correct answer.
  3. 12
  4. 15

Explanation

Original work remaining after 30 days = 50 workers * 90 days = 4,500 worker-days. Due to resignations, there are 40 workers remaining. Time remaining = 90 days. To complete the 4,500 worker-days of work in 90 days, the number of workers needed is 4,500 / 90 = 50 workers. Since we only have 40 workers left, we must hire 50 - 40 = 10 additional workers (which exactly replaces the 10 who resigned).

Question 32Numerical reasoning

A public transit service runs three bus routes. Bus A leaves the terminal every 12 minutes, Bus B every 18 minutes, and Bus C every 30 minutes. If all three buses leave the terminal together at 8:00 AM, at what time will they next leave the terminal together?

  1. 10:00 AM
  2. 11:00 AM Correct answer.
  3. 12:00 PM
  4. 1:00 PM

Explanation

To find the next simultaneous departure, calculate the Least Common Multiple (LCM) of the intervals: 12, 18, and 30 minutes. Prime factors: 12 = 2^2 * 3; 18 = 2 * 3^2; 30 = 2 * 3 * 5. LCM = 2^2 * 3^2 * 5 = 4 * 9 * 5 = 180 minutes. 180 minutes = 3 hours. 8:00 AM + 3 hours = 11:00 AM.

Question 33Numerical reasoning

A ministry splits its IT budget such that 40% is for hardware, 35% for software, and the remaining €75,000 is for cybersecurity training. If the software budget is later reduced by 20% and the saved money is redirected to the cybersecurity training budget, what is the new cybersecurity training budget?

  1. €92,500
  2. €96,000 Correct answer.
  3. €105,000
  4. €120,000

Explanation

The percentage for training is 100% - (40% + 35%) = 25%. Since 25% of the budget is €75,000, the total budget is €75,000 / 0.25 = €300,000. The software budget is 35% of €300,000 = €105,000. The software budget is reduced by 20%: 20% of €105,000 = €21,000. This €21,000 is added to the training budget: €75,000 + €21,000 = €96,000.

Question 34Numerical reasoning

A team of 4 administrative officers can draft a report in 12 hours. If they are joined by 2 technical officers who write at 1.5 times the rate of an administrative officer, how long will it take the expanded team to draft the report?

  1. 6.0 hours
  2. 6.8 hours Correct answer.
  3. 7.2 hours
  4. 8.0 hours

Explanation

Let the rate of an administrative officer be r report-parts per hour. Total work = 4 officers * 12 hours = 48r. The rate of a technical officer is 1.5r. The combined rate of the expanded team = 4 administrative officers * r + 2 technical officers * 1.5r = 4r + 3r = 7r. Time required = Total Work / Combined Rate = 48r / 7r = 48 / 7 = 6.85 hours (which rounds to 6.8 hours).

Question 35Numerical reasoning

In a public lottery, a jar contains 5 red tickets, 3 blue tickets, and 2 green tickets. If 2 tickets are drawn at random without replacement, what is the probability that both tickets are of different colors?

  1. 7/9
  2. 13/18
  3. 7/10
  4. 31/45 Correct answer.

Explanation

Calculate the probability of drawing two tickets of the same color first. Total tickets = 5 + 3 + 2 = 10. Probability of 2 red = (5/10) * (4/9) = 20/90. Probability of 2 blue = (3/10) * (2/9) = 6/90. Probability of 2 green = (2/10) * (1/9) = 2/90. Probability of same color = (20 + 6 + 2) / 90 = 28/90 = 14/45. Probability of different colors = 1 - 14/45 = 31/45.

Question 36Abstract reasoning

Complete the pattern: Circle, Triangle, Square, Circle, Triangle, Square, Circle, ________.

  1. Circle
  2. Triangle Correct answer.
  3. Square
  4. Pentagon

Explanation

The pattern repeats three shapes in order: Circle -> Triangle -> Square. After the Circle, the next shape in the sequence is the Triangle.

Question 37Abstract reasoning

In a sequence of shapes, the number of sides increases by 1 each time: Triangle (3), Square (4), Pentagon (5)... what is the next shape in the sequence?

  1. Hexagon Correct answer.
  2. Heptagon
  3. Octagon
  4. Circle

Explanation

The number of sides increases by 1 at each step: 3 -> 4 -> 5 -> 6. A shape with 6 sides is a Hexagon.

Question 38Abstract reasoning

A grid has a black dot that moves one corner clockwise at each step. If the dot starts at the top-left corner, what is its position in the 4th step?

  1. Top-right corner
  2. Bottom-right corner
  3. Bottom-left corner Correct answer.
  4. Top-left corner

Explanation

Counting the starting position as step 1 and moving one corner clockwise each step: step 1 = top-left, step 2 = top-right, step 3 = bottom-right, step 4 = bottom-left. Therefore at the 4th step the dot is at the bottom-left corner.

Question 39Abstract reasoning

A pattern of arrows points in the following directions: North, East, South, West, North, East, South... what direction is next?

  1. North
  2. East
  3. South
  4. West Correct answer.

Explanation

The arrow rotates 90 degrees clockwise at each step: North -> East -> South -> West. After South, the next direction is West.

Question 40Abstract reasoning

A set of figures shows a circle with lines inside. Figure 1 has 1 vertical line. Figure 2 has 2 horizontal lines. Figure 3 has 3 vertical lines. Figure 4 has 4 horizontal lines. What is the pattern for Figure 5?

  1. 5 vertical lines Correct answer.
  2. 5 horizontal lines
  3. 6 vertical lines
  4. 6 horizontal lines

Explanation

The pattern alternates the line direction (vertical -> horizontal -> vertical -> horizontal -> vertical) and increases the number of lines by 1 at each step (1 -> 2 -> 3 -> 4 -> 5). Therefore, Figure 5 has 5 vertical lines.

Question 41Abstract reasoning

In a sequence of grids, a shaded square shifts one position to the right in each row. When it reaches the end of a row, it moves to the start of the next row. If the grid is 3x3 and the shaded square starts at row 1 column 1, where is it at the 5th step (starting count as 1)?

  1. Row 2 Column 2 Correct answer.
  2. Row 2 Column 1
  3. Row 2 Column 3
  4. Row 3 Column 1

Explanation

Tracing the positions with the start counted as Step 1: Step 1 = R1C1, Step 2 = R1C2, Step 3 = R1C3, Step 4 = R2C1, Step 5 = R2C2. Therefore at the 5th step the shaded square is at Row 2 Column 2.

Question 42Abstract reasoning

A pattern of numbers inside shapes: a triangle (3 sides) contains the number 9; a square (4 sides) contains the number 16; a pentagon (5 sides) contains the number 25. What number is inside a hexagon (6 sides)?

  1. 30
  2. 36 Correct answer.
  3. 42
  4. 49

Explanation

The number inside each shape is the square of the number of sides: 3^2 = 9; 4^2 = 16; 5^2 = 25. For a hexagon with 6 sides, the number inside should be 6^2 = 36.

Question 43Abstract reasoning

An abstract pattern consists of shapes with nested figures. Figure 1: Triangle inside Square. Figure 2: Square inside Pentagon. Figure 3: Pentagon inside Hexagon. What is Figure 4?

  1. Hexagon inside Heptagon Correct answer.
  2. Heptagon inside Hexagon
  3. Pentagon inside Hexagon
  4. Triangle inside Heptagon

Explanation

At each step the inner shape of the new figure is the outer shape of the previous figure (Square -> Pentagon -> Hexagon), and the outer shape gains one side each step (Square 4 -> Pentagon 5 -> Hexagon 6 -> Heptagon 7). Therefore Figure 4 is a Hexagon inside a Heptagon.

Question 44Abstract reasoning

In a sequence of shapes, each figure is rotated 45 degrees counter-clockwise. If the arrow in Figure 1 points North-East, in which direction will the arrow in Figure 4 point?

  1. North
  2. West Correct answer.
  3. South-West
  4. North-West

Explanation

Figure 1: North-East. Figure 2: North (rotated 45 CCW). Figure 3: North-West (rotated 45 CCW). Figure 4: West (rotated 45 CCW). Therefore, the arrow in Figure 4 points West.

Question 45Abstract reasoning

A pattern of dots inside a grid: Grid 1 has 1 dot in the top-left. Grid 2 has 2 dots in the top-right. Grid 3 has 3 dots in the bottom-right. How many dots and where are they in Grid 4?

  1. 4 dots in the bottom-left Correct answer.
  2. 4 dots in the top-left
  3. 5 dots in the bottom-left
  4. 5 dots in the top-right

Explanation

The number of dots increases by 1 at each step: 1 -> 2 -> 3 -> 4. The position of the dots rotates clockwise: Top-left -> Top-right -> Bottom-right -> Bottom-left. Therefore, Grid 4 has 4 dots in the bottom-left corner.

Question 46Abstract reasoning

In a 3x3 matrix, the top row has a circle with 1 line, a circle with 2 lines, a circle with 3 lines. The second row has a square with 2 lines, a square with 3 lines, a square with 4 lines. The third row starts with a triangle with 3 lines, followed by a triangle with 4 lines. What completing shape and lines are at the end of the third row?

  1. Triangle with 4 lines
  2. Triangle with 5 lines Correct answer.
  3. Square with 5 lines
  4. Circle with 5 lines

Explanation

The shape remains constant in each row (Row 1: Circle, Row 2: Square, Row 3: Triangle). The number of lines increases by 1 from left to right in each row (Row 1: 1, 2, 3; Row 2: 2, 3, 4; Row 3: 3, 4, 5). Therefore, the final shape is a Triangle with 5 lines.

Question 47Abstract reasoning

A figure consists of a black circle and a white circle. In each step, the black circle moves 1 unit to the right, and the white circle moves 1 unit down. If they start at the same position (0,0) on a grid, at which step will they be separated by exactly 5 units horizontally and 5 units vertically?

  1. Step 3
  2. Step 4
  3. Step 5 Correct answer.
  4. Step 6

Explanation

After step n, the black circle is at (n, 0) and the white circle is at (0, -n). The horizontal separation between them is n units and the vertical separation is also n units. For both separations to equal 5 units, n must equal 5. Therefore, the circles are 5 units apart along each axis at Step 5.

Question 48Abstract reasoning

In a sequence of shapes, Figure 1 is a solid black square. Figure 2 is a black square with a white circle inside. Figure 3 is a black square with a white circle containing a black triangle inside. What is the pattern for Figure 4?

  1. A black square with a white circle containing a black triangle with a white dot inside Correct answer.
  2. A solid white square
  3. A black circle inside a white square
  4. A white circle containing a black triangle

Explanation

The pattern nests alternating black and white shapes: Square (black) -> Circle (white) -> Triangle (black) -> Dot/Circle (white). Figure 4 must continue this nesting sequence by placing a white shape (a dot or small circle) inside the black triangle.

Question 49Abstract reasoning

A logical matrix has the following rule: Column 3 = Column 1 + Column 2 (where overlapping lines merge and non-overlapping lines are added). If Row 1 Column 1 has a vertical line, and Row 1 Column 2 has a horizontal line, Row 1 Column 3 has a cross (+). If Row 2 Column 1 has a diagonal line (/) and Row 2 Column 3 has an X, what is in Row 2 Column 2?

  1. A vertical line
  2. A horizontal line
  3. A diagonal line (\) Correct answer.
  4. A cross (+)

Explanation

The rule is Column 3 = Column 1 + Column 2. In Row 2, Column 1 has a diagonal line (/) and Column 3 has an X (which consists of / and \). Therefore, Column 2 must contain the missing diagonal line (\) to complete the X.

Question 50Abstract reasoning

A pattern of shapes contains numbers that represent a mathematical relation. A triangle with numbers 2, 3, and 6 at its corners has the number 36 in the center. A square with numbers 2, 2, 3, and 3 at its corners has the number 36 in the center. A pentagon has numbers 1, 2, 2, 3, and 3 at its corners. What number is in the center of the pentagon?

  1. 36 Correct answer.
  2. 72
  3. 108
  4. 144

Explanation

The center number is the product of all the corner numbers. Triangle: 2 * 3 * 6 = 36. Square: 2 * 2 * 3 * 3 = 36. Pentagon: 1 * 2 * 2 * 3 * 3 = 36. Therefore, the center number is 36.