Counting cows

What this counting-and-algebra interview question tests

This is an easy problem that asks you to set up and solve a system of linear equations under real-world constraints. It is typical of the kind of foundational reasoning quant interviews use to check that you can move fluently from a word problem to a mathematical model, and then to a clean answer.

The challenge lies not in the arithmetic, but in translating the relationships between quantities into equations, keeping track of the physical constraints (each animal type has a fixed leg count), and then solving systematically. Interviewers use questions like this to gauge confidence with constraint-based reasoning and attention to detail.

• Setting up variables and constraints from prose
• Solving systems of linear equations
• Validating your answer against the original problem