CAT 2026 Slot 1 DILR Q13: 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.

MCQ · +3 / −1

In how many different ways can the counter serve a customer who prefers ₹500 notes?

Answer and solution

Correct answer: C

Solution

$a + 2b + 5c = 60$ with $c > a + b$:
$c = 12$: (0,0) → 1
$c = 11$: (5,0), (3,1), (1,2) → 3
$c = 10$: (8,1), (6,2), (4,3), (2,4), (0,5) → 5 [(10,0) fails]
$c = 9$: (1,7) → 1
Total $= 10$

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