CAT 2026 Slot 1 DILR Q14: 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

If the counter can serve only 10 customers with a stock of 60 ₹500 notes and a sufficient number of notes of other denominations, what is the maximum number of customers who can have ₹500 notes as their preference?

Your answer

Answer and solution

Correct answer: 6

Solution

Fewest ₹500 notes for a ₹500-preferring customer is 9 ($1 \times ₹100 + 7 \times ₹200 + 9 \times ₹500$; $9 > 8$). [Doc said 10 — corrected; answer unchanged.]
$\lfloor 60/9 \rfloor = 6$ customers. The other 4 can be served with no ₹500 notes (e.g. 30 × ₹200).

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