Numerical patterns Transitional Reasoning Practice

Questions

1. 1.

   A newly renovated concert hall features an auditorium with 24 numbered rows of seats arranged in order from the stage. The first row contains 18 seats, and each subsequent row contains 4 more seats than the row directly in front of it, establishing a constant numerical pattern. To ensure spacious seating, event organizers decide to reserve every row that contains strictly more than 50 seats for visiting delegates. How many rows in the auditorium are reserved for visiting delegates?

   • A) 14
   • B) 16
   • C) 15
   • D) 9
2. 2.

   A laboratory microbiologist monitors the growth of a bacterial culture across consecutive incubation cycles. The count of colony-forming units follows a numerical pattern where each cycle multiplies the previous count by a constant factor, recording 16 units in Cycle 1, 48 units in Cycle 2, and 144 units in Cycle 3. Laboratory protocols mandate that an automated nutrient dispenser must shut off during the first incubation cycle in which the colony count exceeds 3,500 units. During which incubation cycle will the nutrient dispenser shut off?

   • A) Cycle 5
   • B) Cycle 6
   • C) Cycle 7
   • D) Cycle 8
3. 3.

   A telecommunications engineer configures signal amplifiers placed at numbered posts along a fiber-optic transmission line. The amplification gain set at each post follows a numerical pattern with a constant difference, where Post 4 is set to 31 decibels and Post 10 is set to 67 decibels. Due to safety specifications, an amplifier cannot be configured to a gain exceeding 100 decibels. What is the maximum amplification gain, in decibels, that the engineer can configure on this line?

   • A) 85 decibels
   • B) 91 decibels
   • C) 97 decibels
   • D) 100 decibels
4. 4.

   A quality control technician inspects serialized metallic components along an automated assembly line. Each approved component is stamped with an identification code that follows a numerical pattern with a constant difference between consecutive components. Component 5 is stamped with code 41, and Component 12 is stamped with code 90. Which of the following identification codes could NOT belong to a component produced on this assembly line?

   • A) 132
   • B) 174
   • C) 202
   • D) 243
5. 5.

   A robotics research team tests an autonomous rover by running it along a straight course across consecutive numbered stages. The distance the rover travels in each stage follows a numerical pattern with a constant increase from one stage to the next. In Stage 8, the rover travels exactly three times as far as it does in Stage 2, and in Stage 5, it travels a distance of 42 meters. What is the distance, in meters, that the rover travels in Stage 1?

   • A) 21 meters
   • B) 18 meters
   • C) 28 meters
   • D) 14 meters
6. 6.

   A community library hosts an annual reading marathon where students earn reward tokens according to the number of chapters completed, following a constant numerical pattern. A student who completes 4 chapters earns 31 tokens, while a student who completes 9 chapters earns 66 tokens. If two siblings participate in the marathon and complete 6 chapters and 11 chapters, respectively, how many reward tokens do the two siblings earn altogether?

   • A) 119 tokens
   • B) 122 tokens
   • C) 125 tokens
   • D) 139 tokens
7. 7.

   A specialized print shop manufactures numbered commemorative booklets for a university archive in scheduled production runs. The quantity of booklets produced follows a constant numerical pattern across the runs. The total combined production of Run 3 and Run 7 is 196 booklets, while Run 9 yields 122 booklets. How many booklets are produced in Run 1?

   • A) 68
   • B) 82
   • C) 86
   • D) 74
8. 8.

   A structural engineering laboratory measures the load-bearing capacity of modular steel trusses across consecutive design iterations. The maximum supported load follows a constant numerical pattern, registering 43 kilonewtons for Iteration 2 and 79 kilonewtons for Iteration 5. Quality protocols mandate that specialized vibration dampers must be installed only on trusses that support more than 100 kilonewtons but no more than 130 kilonewtons. Which design iteration is the last one eligible for the installation of vibration dampers?

   • A) Iteration 7
   • B) Iteration 8
   • C) Iteration 10
   • D) Iteration 9
9. 9.

   An aerospace engineering team tests a turbine combustion chamber across a sequence of numbered operational cycles. The chamber temperature increases following a constant numerical pattern, reaching 35 degrees Celsius at Cycle 4 and 50 degrees Celsius at Cycle 7. A thermal safety sensor is programmed to activate during the cycle when the temperature reaches exactly double the temperature recorded at Cycle 3. At which operational cycle will the thermal safety sensor activate?

   • A) Cycle 6
   • B) Cycle 8
   • C) Cycle 9
   • D) Cycle 12
10. 10.

    A precision manufacturing laser is programmed to engrave metallic test strips with barcodes whose total scan time increases following a constant numerical pattern as the barcode density increases. The scan time is 29 milliseconds for a density level of 4 and 53 milliseconds for a density level of 8. If $n$ represents the barcode density level, which expression gives the scan time, in milliseconds, at density level $n$?

    • A) $4n + 13$
    • B) $8n - 3$
    • C) $6n + 5$
    • D) $5n + 13$
11. 11.

    A clean-energy testing facility configures modular storage arrays where both the energy capacity and the number of interconnected modules increase following constant numerical patterns. Configuration 1 delivers an energy capacity of 19 kilowatt-hours using 4 modules, Configuration 2 delivers 31 kilowatt-hours using 7 modules, and Configuration 3 delivers 43 kilowatt-hours using 10 modules. If an industrial simulation requires an energy capacity of exactly 115 kilowatt-hours, how many interconnected modules must be deployed in that configuration?

    • A) 25 modules
    • B) 28 modules
    • C) 31 modules
    • D) 34 modules
12. 12.

    An industrial wastewater purification facility operates five consecutive filtration stages where the volume of water processed follows a decreasing numerical pattern. Each stage after the first processes exactly 12 cubic meters less wastewater than the stage immediately before it. If the facility processes a total combined volume of 380 cubic meters across all five stages, how many cubic meters of wastewater are processed at Stage 5?

    • A) 52 cubic meters
    • B) 64 cubic meters
    • C) 76 cubic meters
    • D) 40 cubic meters
13. 13.

    An automated distribution warehouse dispatches parcels in numbered cargo containers according to a constant numerical pattern. The first three containers carry 14, 22, and 30 parcels, respectively. If two consecutive containers carry a combined total of 356 parcels, what is the container number of the earlier container?

    • A) 20
    • B) 21
    • C) 22
    • D) 23
14. 14.

    An agricultural cooperative monitors the total mass of organic fertilizer stored in a central silo throughout a planting season. At the end of Cycle 4, the silo contains 418 tonnes of fertilizer, and at the end of Cycle 10, the silo contains 262 tonnes. If the fertilizer is consumed according to a constant numerical pattern each cycle, what was the initial mass of fertilizer in the silo before Cycle 1 began?

    • A) 522 tonnes
    • B) 496 tonnes
    • C) 574 tonnes
    • D) 314 tonnes
15. 15.

    An urban landscaping project plants saplings along concentric circular zones according to an expanding numerical pattern. The team plants 8 saplings in Zone 1, 15 saplings in Zone 2, 24 saplings in Zone 3, and 35 saplings in Zone 4. If this numerical pattern continues according to the same rule, how many saplings will be planted in Zone 8?

    • A) 99 saplings
    • B) 80 saplings
    • C) 120 saplings
    • D) 79 saplings
16. 16.

    An environmental monitoring station tracks the concentration of dissolved oxygen in an experimental wetland basin at regular 3-hour recording intervals. The recorded oxygen levels follow a constant decreasing numerical pattern, registering 82 milligrams per liter at Hour 6 and 58 milligrams per liter at Hour 18. An automated aeration pump activates during the scheduled recording when the dissolved oxygen level first falls below 30 milligrams per liter. At which recording hour will the aeration pump first activate?

    • A) Hour 30
    • B) Hour 33
    • C) Hour 36
    • D) Hour 39
17. 17.

    A structural engineering team monitors the load-bearing capacity of a reinforced support column during a series of staged pressure tests. The test measurements follow a constant numerical pattern, with Phase 4 recording a capacity of 51 kilonewtons and Phase 9 recording a capacity of 86 kilonewtons. If the testing procedure continues according to this established pattern, what will be the recorded capacity during Phase 16?

    • A) 135 kilonewtons
    • B) 121 kilonewtons
    • C) 142 kilonewtons
    • D) 128 kilonewtons
18. 18.

    Two community greenhouse projects track their total number of planted herb containers following constant daily numerical patterns. Garden Alpha starts on Day 1 with 45 containers and adds 14 new containers each following day, while Garden Beta starts on Day 1 with 117 containers and adds 8 new containers each following day. If both community gardens continue adding containers according to these established linear patterns, on which day will both gardens have an identical number of containers?

    • A) Day 10
    • B) Day 12
    • C) Day 13
    • D) Day 14
19. 19.

    A municipal recycling depot records the mass of sorted electronic waste collected each week. During the first four weeks, the depot collects 26 tonnes, 33 tonnes, 40 tonnes, and 47 tonnes, respectively, establishing a constant weekly increase. If this numerical pattern continues at the same rate, in which week will the depot collect exactly 110 tonnes of electronic waste?

    • A) Week 13
    • B) Week 12
    • C) Week 14
    • D) Week 15

Answers and step-by-step solutions appear after you finish the test.