Pattern 19·Advanced·L3

Multiple Group Percentage Change

Medium FrequencyImportant 90–120 sec

USE WHEN

Different subgroups change by different percentages and total change is asked.

BEST METHOD

Weighted Change Method

TARGET

90–120 sec

MASTERY

not started

Recognition Cues

subgroups change differently
overall change asked
weighted overall percentage

How to Recognise

Different subgroups change by different percentages and total change is asked.

Core Concept

Overall change is a weighted average of subgroup percentage changes, weighted by original subgroup sizes.

Overall \% change = Σ(weight \times subgroup \% change), where weights sum to 1.

Athena Shortcut

Choose an original total of 100 and split using group shares.

Alternative Method · Weighted Change Method

Use weighted average of subgroup percentage changes.

Timed drill

Identify the base or invariant before you calculate.

2:00

Attempt first · Standard Example

60% of staff are A and 40% are B. A rises 10%, B falls 5%. Overall change?

Attempt first · CAT-Level Example

A firm has departments in ratio 2:3:5. Their headcounts change by +20%, −10%, +5%. Find overall % change.

Common Trap

Do not average the percentage changes arithmetically unless subgroup sizes are equal.

3-level practice ladder

Attempt all three before checking solutions

Foundation

Two groups are in ratio 1:4. The first grows 25% and the second falls 5%. Find overall percentage change.

CAT Standard

Three departments are in ratio 2:3:5 and change by +20%, −10% and +5%. Find overall percentage change.

Advanced / Hybrid

40% of employees belong to A and 60% to B. A grows 15% while B falls 5%. Find total workforce change.

PYQ Mapping

Verified mappingCAT 2019 · Slot 2

cat 2019 slot 2: fiction and non-fiction categories grow by different percentages while total changes.

Pattern Connections

#15 Percentage Distribution #25 Percentage + Average #26 Percentage + Profit / Loss

Core Concept

Overall change is a weighted average of subgroup percentage changes, weighted by original subgroup sizes.

Overall \% change = Σ(weight \times subgroup \% change), where weights sum to 1.

Attempt all three before checking solutions

Foundation

Two groups are in ratio 1:4. The first grows 25% and the second falls 5%. Find overall percentage change.

CAT Standard

Three departments are in ratio 2:3:5 and change by +20%, −10% and +5%. Find overall percentage change.

Advanced / Hybrid