Percentage of, Percentage comparison and Percentage change

Question

This seems like an easy topic, however I found a caveat in my understanding while solving questions. So I tried to deeply understand the nuances amongst the translation of these 3 topics. Here is an ultimate guide that brings together  Percentage of ,  Percentage Comparison , and  Percentage Change  in one place

🚀 Ultimate Percentage Cheat Sheet 
    Aspect  
  Percentage of  🌗 
  Percentage Comparison  ⚖️ 
  Percentage Change  🔄 
 
   Purpose  
 Find a part of a whole 
 Compare two values (how much more/less) 
 Measure increase or decrease over time 
 
   Key Question  
 “What is X% of Y?” 
 “By what % is A more/less than B?” 
 “By what % did the value increase/decrease?” 
 
   Focus  
 Portion of a total 
 Difference between two values 
 Change from an original value 
 
   Formula  
 (Part/Whole)×100

OR X% of Y  
 (Difference/ Reference)×100 
 (New−Old)/Old×100 
 
   Reference Point  
 The  whole  (total amount) 
 The value  after "than"  (comparison base) 
 The  original/old value  (starting point) 
 
   Context  
 Discounts, tax, marks scored 
 Price comparisons, salary gaps 
 Stock price changes, population growth 
 
   Example  
 “What is 25% of 200?” →  50  
 “How much more is 150 than 100?” →  50%  
 “Price increased from 100 to 150?” →  50%  
 
   Output Type  
 A  specific value  
 A  percentage difference  
 A  percentage increase/decrease

🔑  Quick Memory Hacks: 
 
  “Of” = Portion of a Whole  
  “Comparison” = Difference Between Two Values  
  “Change” = Tracking Growth or Decline Over Time

Hope this is helpful!

Archit3110 · Answer

Not sure whether topic tagging is correct done...

nishantswaft · Answer

GMAT tests this concept very frequently, kudos for compiling it as a comprehensive table.

undetenetur · Answer

The easiest way to never get confused between % increase and % decrease is this:
 Always divide by the original value. 
That’s it. That’s the rule.
🔹 Percent Increase Formula
New−OldOld×100\frac{	ext{New} - 	ext{Old}}{	ext{Old}} 	imes 100OldNew−Old×100
🔹 Percent Decrease Formula
Old−NewOld×100\frac{	ext{Old} - 	ext{New}}{	ext{Old}} 	imes 100OldOld−New×100
Notice something?
The denominator (bottom number) is ALWAYS the original value.
 
Example (mental math friendly):
Price goes from 200 → 250
Difference = 50
50 ÷ 200 = 0.25
0.25 × 100 =  25% increase 
 
Quick brain trick:
Instead of doing full division, think in fractions:
If something goes from 80 → 100
Difference = 20
20 is  1/4 of 80 
1/4 = 25%
So it’s a 25% increase.
 
Why people get confused
When values switch, they accidentally divide by the wrong base.
Example:
100 → 80 is a 20% decrease
But 80 → 100 is NOT 20% increase
It’s 25% increase (because you divide by 80).
The base always changes depending on what you're comparing  from .
 
If you want to double-check your steps while practicing, you can plug numbers into something like this percentage increase calculator:
Mumbaipuneportal
But honestly, once you lock in the “difference ÷ original” rule, it becomes automatic.
After 10–15 practice problems, your brain starts seeing the fraction instantly.

Percentage of, Percentage comparison and Percentage change

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Aspect	Percentage of 🌗	Percentage Comparison ⚖️	Percentage Change 🔄
Purpose	Find a part of a whole	Compare two values (how much more/less)	Measure increase or decrease over time
Key Question	“What is X% of Y?”	“By what % is A more/less than B?”	“By what % did the value increase/decrease?”
Focus	Portion of a total	Difference between two values	Change from an original value
Formula	(Part/Whole)×100 OR X% of Y	(Difference/ Reference)×100	(New−Old)/Old×100
Reference Point	The whole (total amount)	The value after "than" (comparison base)	The original/old value (starting point)
Context	Discounts, tax, marks scored	Price comparisons, salary gaps	Stock price changes, population growth
Example	“What is 25% of 200?” → 50	“How much more is 150 than 100?” → 50%	“Price increased from 100 to 150?” → 50%
Output Type	A specific value	A percentage difference	A percentage increase/decrease

GMAT Problem Solving (PS) Questions

Percentage of, Percentage comparison and Percentage change

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