Ratios, Percentages, Averages and Population notes for CAT: 106 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.
A clean journey from comparison to CAT-level arithmetic modelling.
You master part-to-part comparison, shifting, sharing, age ratios, salary ratios, and mixture-style split logic.
You learn increase, decrease, successive change, and population-style growth logic.
You convert averages into totals and use weighted average thinking for groups and constraints.
You combine category counts with percentages, ratios, and table-based thinking.
The art of converting comparison stories into equations.
Means the quantities are and , not necessarily 3 and 2.
The multiplier is found from extra information: total, difference, shift, or final ratio.
If , then
If , then total parts are .
If and :
parts
So part , hence , .
The average of seven numbers is . What is the total of the seven numbers?
63
Key idea: the total method says convert an average into a hidden total by multiplying average by count.
Step 1: Use .
Step 2: Average , Count .
Step 3: Total .
Answer: .
In competitive exams, when a problem provides the average of a set and the number of items in the set, what is the most powerful "hidden" quantity you should immediately calculate?
A
Key idea: this is a total-method trigger question, recognisable because both the average and the count are explicitly given.
Step 1: The formula connecting average, total, and count is .
Step 2: Rearranging this gives .
Step 3: In average problems, the total sum is the most useful hidden quantity because it allows you to combine groups, track changes, or apply constraints.
Answer: The total sum.
Ratios, Percentages, Averages and Population notes for CAT: 106 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questi
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