CAT 2026 Slot 1 DILR Q12: Maths-based / Combinations

The set

A cash counter distributes exactly ₹6,000 per transaction using ₹100, ₹200 and ₹500 notes. Each customer specifies one of these three denominations as their preferred denomination. The counter distributes notes such that the number of notes of the customer's preferred denomination exceeds the total number of notes of the other two denominations.

TITA (type the answer) · +3 / 0

What is the maximum number of customers that the counter can serve with a stock of fifty ₹500 notes and a sufficient number of notes of other denominations, if all customers are to be served with at most 20 notes per transaction?

Your answer

Answer and solution

Correct answer: 7

Solution

Prefer ₹100 needs at least 23 notes — impossible within 20.
Prefer ₹200 within 20 notes: fewest ₹500 notes is 7 ($a = 1, b = 12, c = 7$; $12 > 8$).
Prefer ₹500 needs at least 9 ₹500 notes.
So 7 per customer: $\lfloor 50/7 \rfloor = 7$ customers.

An expected paper by Cetking, not the actual CAT paper. CAT is conducted by the IIMs.