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 13·Core CAT·L2

Marks / Pass–Fail

Medium FrequencyImportant 60–90 sec

USE WHEN

Passing percentage, marks short/excess, maximum marks or two students' outcomes are linked.

BEST METHOD

Difference Equation Method

TARGET

60–90 sec

MASTERY

not started

Recognition Cues

  • pass marks, fail by, exceeds by
  • maximum marks or pass percentage
  • compare two candidates

How to Recognise

Passing percentage, marks short/excess, maximum marks or two students' outcomes are linked.

Core Concept

Translate every mark condition into a percentage of total maximum marks.

Marks=(%/100)×Maximum;usedifferenceofequationstoeliminatethepassmark.Marks = (\%/100)\times Maximum; use difference of equations to eliminate the pass mark.Marks=(%/100)×Maximum;usedifferenceofequationstoeliminatethepassmark.

Athena Shortcut

When two candidates miss/exceed pass marks by known amounts, subtract their percentage equations.

Alternative Method · Difference Equation Method

Use the score gap between two candidates to eliminate the pass mark.

Timed drill

Identify the base or invariant before you calculate.

1:30

Attempt first · Standard Example

Pass mark is 40% of 500. Find pass marks.

Attempt first · CAT-Level Example

A candidate scoring 35% fails by 20 marks, while another scoring 45% gets 30 marks above pass marks. Find maximum marks.

Common Trap

  • ‘Fails by 20’ refers to the gap from the pass mark, not 20% of anything.

3-level practice ladder

Attempt all three before checking solutions

Foundation

A candidate scoring 30% fails by 24 marks, while another scoring 42% exceeds the pass mark by 12 marks. Find maximum marks.

CAT Standard

A student scoring 35% fails by 30 marks; another scoring 50% gets 15 marks above pass marks. Find maximum marks.

Advanced / Hybrid

Two students score 48% and 64% of maximum marks. The second scores 36 marks more. What would 80% of the maximum be?

PYQ Mapping

Verified mappingCAT 2020 · Slot 3

cat 2020 slot 3: exam scores given as percentages with mark differences used to reconstruct another score.

Pattern Connections

#15 Percentage Distribution #23 Percentage Equations #32 Multi-Constraint CAT Percentage Problems
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.