Solve 310+ Ratios, Percentages, Averages and Population practice questions for CAT with answers and detailed solutions. Free sample questions below.
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.
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.
Which of the following phrases in an averages word problem is the strongest trigger to immediately apply the Total Method?
C
Key idea: this is a pattern-recognition question, recognisable because it asks for the specific trigger condition of a core method.
Step 1: The Total Method relies on the equation .
Step 2: To use this equation, you must be given (or be able to deduce) both the average and the count of a specific group.
Step 3: Therefore, seeing both the average and the count provided in the problem is the direct trigger to calculate the hidden total.
Answer: The average and the count of a group are both given.
A team of employees has an average annual bonus of \3,000\ to every employee's bonus. What is the new average annual bonus?
3500
Key idea: Adding a constant value to every item in a dataset increases the average by exactly that constant.
Step 1: Identify the original average and the uniform change. Original average = \3,000\.
Step 2: Apply the constant-shift property. New average = Original average + Constant added = .
Step 3: Calculate. .
Answer: 3500
A set of at least two numbers has average . Which of the following transformations will definitely leave the average unchanged?
["A","D"]
Key idea: this is an average-invariance question. The trigger is that the question asks which transformations preserve the average for any set with average .
Let the set have numbers and total . Since the average is ,
Step 1: Test option A.
Each becomes .
New total:
Substitute :
New average:
So option A preserves the average.
Step 2: Test option B.
Each becomes .
New total:
New average is , not necessarily .
So option B does not definitely preserve the average.
Step 3: Test option C.
Each becomes .
New total:
New average is , not necessarily .
So option C does not definitely preserve the average.
Step 4: Test option D.
Adding to one number and subtracting from another changes the total by
The count is unchanged, so the average is unchanged.
Option D preserves the average.
Answer: A and D.
Trap: subtracting from every number does not preserve the original average; it shifts the average to . Preservation depends on how the total changes, not on how individual expressions look.
Solve 310+ Ratios, Percentages, Averages and Population practice questions for CAT with answers and detailed solutions. Free sample questions below.
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