Guide
Average questions often hide ratio, replacement, weighted-average or DI logic rather than test the basic formula directly. For CAT preparation, the useful question is not “Have I finished the chapter?” but can I recognise the version of the concept CAT hides inside a word problem and choose an efficient method under time pressure?
What to know
The core checklist for this topic is: Arithmetic mean, weighted average, combined average, replacement, deviation from mean, average speed distinction. Learn these as connected ideas rather than isolated formulas. CAT often combines two of them in one question.
Recurring CAT-style forms
Expect questions built around Member joins/leaves group, one value replaced, combined groups, average after increment, weighted score, and missing value from average. The wording changes, but the mathematical structure repeats. Your first 20–30 seconds should be spent identifying that structure before writing equations.
Decision rules worth remembering
- Total = average × count
- change in total = count × change in average
- combined average is weighted
- average speed generally uses total distance/total time
One original example
A class of 20 has average 60. A class of 30 has average 70. Combined average is (20×60+30×70)/50=66, not 65, because the groups have different sizes.
The point of a worked example is not the answer; it is the choice of representation. After solving, ask whether a ratio table, base-100 assumption, sign chart, factorisation or diagram made the work shorter.
Common traps
- Averaging two averages without weights
- using arithmetic mean for equal-distance speeds
- forgetting group size changes
- treating median as average
These traps are valuable because they explain why a student can “know the formula” and still lose marks. Add the exact mistake to your error log when it occurs; do not simply write “silly mistake.”
How to practise
Start with 10–15 untimed questions until the first step becomes automatic. Then use mixed timed sets where this topic is not announced in advance. Finish with sectionals and mock review. Mastery checkpoint: Can solve most replacement/combined-average questions through total-change logic in under 2 minutes.
Once that checkpoint is stable, move on rather than over-polishing one chapter. CAT QA is a portfolio of scoring areas; the objective is enough reliable topics to make question selection easy on exam day.
Preparing for CAT?
See where you actually stand before changing your shortlist or study plan.
Why On Your Mocks?
A mock score tells you what happened. OYM helps you understand what went wrong and what to work on next.