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Pattern 11·Core CAT·L2

Population Growth / Decline

Medium FrequencyImportant 60–90 sec

USE WHEN

Population, users, customers, production or membership changes year by year.

BEST METHOD

Reverse Multiplier Method

TARGET

60–90 sec

MASTERY

not started

Recognition Cues

  • population/users/growth over years
  • annual increase/decrease
  • final count after multiple years

How to Recognise

Population, users, customers, production or membership changes year by year.

Core Concept

Repeated population changes are compound percentage changes.

Final=Initial×∏(1±r/100)Final = Initial \times ∏(1±r/100)Final=Initial×∏(1±r/100)

Athena Shortcut

Work with multipliers; only calculate the actual population at the end if needed.

Alternative Method · Reverse Multiplier Method

If final population is given, divide by the compounded growth factor.

Timed drill

Identify the base or invariant before you calculate.

1:30

Attempt first · Standard Example

A town of 40,000 grows 10% in one year. Population?

Attempt first · CAT-Level Example

A town grows 20% in year 1 and declines 10% in year 2. If final population is 59,400, find initial.

Common Trap

  • 20% growth and 10% decline do not mean net 10% growth.

3-level practice ladder

Attempt all three before checking solutions

Foundation

A population increases 10% in each of two consecutive years. Find the net increase.

CAT Standard

A town of 80,000 grows 15% and then declines 10%. Find final population.

Advanced / Hybrid

A town grows 10% in each of two years and ends at 106,480. Find the initial population.

PYQ Mapping

Verified mappingCAT 2023 · Slot 3

cat 2023 slot 3: population falls by y% and then rises by x%, subject to a final-population constraint.

Pattern Connections

#07 Successive Percentage Changes #12 Appreciation / Depreciation #30 Percentage + SI / CI
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Learning flow

  1. 1Recognition Cues
  2. 2How to Recognise
  3. 3Core Concept
  4. 4Formula
  5. 5Athena Shortcut
  6. 6Alternative Method
  7. 7Timed Drill
  8. 8Standard Example
  9. 9CAT-Level Example
  10. 10Common Trap
  11. 11Practice Ladder
  12. 12PYQ Mapping
  13. 13Connections
  14. 14Mastery

Attempt every example before opening its answer.