CAT 2024 Slot 1 QA Question 3

Type-in-the-answer (no negative marking) · Arithmetic · Mean, Median & Mode · Try it, then check the answer and solution below.

CAT 2024 Slot 1QAArithmetic • Mean, Median & ModeModerate

There are four numbers such that average of first two numbers is 1 more than the first number, average of first three numbers is 2 more than average of first two numbers, and average of first four numbers is 3 more than average of first three numbers. Then, the difference between the largest and the smallest numbers, is

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Official Convenor Answer Key: 15

Verified Solution:

### Core Concept We are dealing with averages and their relationships. The key is to set up equations based on the given conditions and solve for the variables step by step.

### Step-by-Step Solution

Let the four numbers be

a, b, c, d

First condition:

Average of first two numbers is 1 more than the first number.

\frac{a + b}{2} = a + 1

Multiply both sides by 2:

a + b = 2a + 2

Subtract

a

b = a + 2

Second condition:

Average of first three numbers is 2 more than average of first two.

\frac{a + b + c}{3} = \frac{a + b}{2} + 2

Substitute

a + b = 2a + 2

\frac{2a + 2 + c}{3} = a + 1 + 2

Simplify RHS:

a + 3

Multiply both sides by 3:

2a + 2 + c = 3a + 9

Answer and solution

Answer: 15

### Core Concept We are dealing with averages and their relationships. The key is to set up equations based on the given conditions and solve for the variables step by step.

### Step-by-Step Solution

Let the four numbers be

a, b, c, d

First condition:

Average of first two numbers is 1 more than the first number.

\frac{a + b}{2} = a + 1

Multiply both sides by 2:

a + b = 2a + 2

Subtract

a

b = a + 2

Second condition:

Average of first three numbers is 2 more than average of first two.

\frac{a + b + c}{3} = \frac{a + b}{2} + 2

Substitute

a + b = 2a + 2

\frac{2a + 2 + c}{3} = a + 1 + 2

Simplify RHS:

a + 3

Multiply both sides by 3:

2a + 2 + c = 3a + 9

Keep going

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