CAT 2023 Slot 2 QA Question 15

Multiple choice (+3 / −1) · Algebra · Linear Equation · Try it, then check the answer and solution below.

CAT 2023 Slot 2QAAlgebra • Linear EquationModerate

If certain amount of money is divided equally among n person, each one receives Rs

352

. However, if two persons receive Rs 506 each and the remaining amount is divided equally among the other persons, each of them received less than or equal to Rs

330

. Then, the maximum possible value of

n

Practice More Questions

⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution

Official Convenor Answer Key: B

Answer and solution

Answer: B) 16

📌 Core Concept

The problem involves dividing a total amount of money in two different scenarios. We use linear equations and inequalities to find the maximum number of people,

n

🔢 Step-by-Step Solution

Total Amount Calculation:

When divided equally among

n

people: Total = 352n$.

Second Distribution Scenario:

Two people receive Rs 506 each: Total given = 2 × 506 = 1012$.

Remaining amount = 352n - 1012$.

This is divided among

n - 2

people: Each person gets

\frac{352n - 1012}{n - 2}

Inequality Setup:

Each person gets ≤ Rs 330:

\frac{352n - 1012}{n - 2} \leq 330

Solving the Inequality:

Multiply both sides by

n - 2

(positive, so inequality sign remains):

352n - 1012 \leq 330(n - 2)

Expand and simplify:

352n - 1012 \leq 330n - 660

22n \leq 352

n \leq 16

Verification:

For

n = 16

: Total = 352 × 16 = 5632$.

After giving 1012, remaining = 4620.

Divided by 14: $4620 / 14 = 330 , which is valid.

For

n = 17

: Each person gets more than 330, which is invalid.

⚡ 30-Second Shortcut

Set up the inequality

\frac{352n - 1012}{n - 2}

≤ 330$.

Solve to find

n \leq 16

Check

n = 16

is valid, so maximum

n

is 16.

🎯 Final Answer

Correct Answer: Option B

CAT 2023 Slot 2 QA Question 15

Keep going

Related Linear Equation questions