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Pattern 22·Advanced·L3

Repeated Percentage Operations

High FrequencyMust Master 90–120 sec

USE WHEN

Several increases, decreases, markups, discounts or growth rates occur in sequence.

BEST METHOD

Net Multiplier Method

TARGET

90–120 sec

MASTERY

not started

Recognition Cues

  • many sequential operations
  • chain of rates
  • compress using multipliers

How to Recognise

Several increases, decreases, markups, discounts or growth rates occur in sequence.

Core Concept

Represent every operation as a multiplier and multiply them in order.

Final=Initial×∏multipliersFinal = Initial \times ∏ multipliersFinal=Initial×∏multipliers

Athena Shortcut

Cancel reciprocal factors early: ×1.25 and ×0.8 cancel exactly.

Alternative Method · Net Multiplier Method

Convert every change into a multiplier and multiply left to right.

Timed drill

Identify the base or invariant before you calculate.

2:00

Attempt first · Standard Example

A value ×1.2, then ×0.9, then ×1.1. Net change?

Attempt first · CAT-Level Example

A price is raised 50%, discounted 20%, then discounted 10%. Compare final price to original.

Common Trap

  • Do not compress successive rates by arithmetic addition.

3-level practice ladder

Attempt all three before checking solutions

Foundation

A value changes by +25%, −20%, then +10%. Find net change.

CAT Standard

A price is marked up 50%, discounted 20%, then discounted 10%. Compare final price with original cost base.

Advanced / Hybrid

A quantity falls 20%, rises 25%, then rises 10%. Find net change.

PYQ Mapping

Verified mappingCAT 2024 · Slot 3

cat 2024 slot 3 successive salary increments; cat 2021 slot 2 loss-growth investment also uses chained multipliers.

Pattern Connections

#07 Successive Percentage Changes #12 Appreciation / Depreciation #26 Percentage + Profit / Loss
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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.