AthenaPrepAthenaPrep

Menu

HomeLearnQuant Blueprints
FlashcardsConcept MapsPYQsMocksFocus
1:1 MentorshipQuantify CATRevision Resources
Refer & Earn
AthenaPrepAthenaPrep

Menu

HomeLearnQuant Blueprints
FlashcardsConcept MapsPYQsMocksFocus
1:1 MentorshipQuantify CATRevision Resources
Refer & Earn
AProfile
Back to Percentage Blueprint
Pattern 17·Advanced·L3

Changing Percentage Base

High FrequencyMust Master 90–120 sec

USE WHEN

Percentages refer to different bases across statements.

BEST METHOD

Layered Base Method

TARGET

90–120 sec

MASTERY

not started

Recognition Cues

  • percentages stacked on different bases
  • A of B and B of C
  • needs base alignment

How to Recognise

Percentages refer to different bases across statements.

Core Concept

Always convert each percentage statement into an equation with its own explicit base.

IfA=x%BandB=y%C,thenA=(x/100)(y/100)C.If A=x\%B and B=y\%C, then A=(x/100)(y/100)C.IfA=x%BandB=y%C,thenA=(x/100)(y/100)C.

Athena Shortcut

Use 100 as the lowest-level base, then build upward.

Alternative Method · Layered Base Method

Start from the deepest base and build upward through multipliers.

Timed drill

Identify the base or invariant before you calculate.

2:00

Attempt first · Standard Example

A is 20% more than B and B is 25% more than C. How much more is A than C?

Attempt first · CAT-Level Example

A is 20% less than B, B is 50% more than C, and C is 20% less than D. Express A as % of D.

Common Trap

  • Do not combine percentages until their bases are aligned.

3-level practice ladder

Attempt all three before checking solutions

Foundation

A is 125% of B and B is 80% of C. A is what percentage of C?

CAT Standard

A is 20% less than B; B is 50% more than C; C is 20% less than D. A is what percentage of D?

Advanced / Hybrid

A is 10% less than B, B is 25% more than C, and C is 20% less than D. Compare A and D.

PYQ Mapping

Verified mappingCAT 2019 · Slot 2

cat 2019 slot 2: a is 10% below b, b 25% above c, c 20% below d; changing-base chain.

Pattern Connections

#06 More Than / Less Than #23 Percentage Equations #24 Percentage + Ratio
Sign in to save progressAll patterns

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.