Opera solutions is a consulting firm which engages in management consulting and decision analytics. The role of Analytics Specialist that Opera offers requires thorough knowledge of Statistics and other topics like Machine Learning. The shortlisting procedure was done through 2 pen-and-paper tests:
Objective Paper (20 questions, 45 minutes)
Consisted of questions on probability theory and basic statistics. Also there were some questions on Data interpretation (similar to those asked in IIM-CAT).
Subjective Paper (6 questions, 45 minutes)
1) A and B play a game. They roll 2 dice every time and add the numbers that show up. If it's a 12, then A wins. If there are 2 consecutive 7's then B wins. With what probability does A win the game?
2) 100 prisoners hat puzzle
3) Prove that product of 4 consecutive numbers is always of the form k^2 - 1.
4) Prove that there always exists a sequence of length n of composite numbers for all n.
5) Geometry problem: 3 circles tangent to each other, find c in terms of a,b. (Sorry I don't remember the diagram)
6) There is a parking space of length 4. Cars come and randomly choose any position to park over the interval [0, 4]. Each car occupies a space of length 1. Calculate expected number of cars that can park.