Optiver Math Test: Subjective Questions

I have posted the subjective questions asked in Optiver's written test below. Do check out Optiver Objective Questions for objective questions asked in the test. Also, if you need more information on Optiver and it's selection procedure check About Optiver.

1) After a snail racing contest, the four contestants were congratulating each other. Only one snail wore the same number as the position it finished in. Alfred's snail wasn't painted yellow nor blue, and the snail who wore 3, which was painted red, beat the snail who came in third. Arthur's snail beat Anne's snail, whereas Alice's snail beat the snail who wore 1. The snail painted green, Alice's, came second and the snail painted blue wore number 4. Anne's nail wore number 1. Can you work out who's snail finished where, it's number and the colour it was painted?

2) At a certain time between 3pm and 4pm, the hour and the minute hands are at equal angles from the 6 mark, what time will it be exactly?

3) I lived in a city that held as much as it could,
    So I moved to another that repaid what what it should.
    The third had very little, with not much to be found,
    The fourth was very boring, with no change in the sound.
    The fifth was so foggy you could not see past the next face.
    The sixth was on the move; I could barely keep up the pace,
    The seventh was strange; bizzare character would people attain,
    So I settled in the eighth, because it was so plain. 
    What are the various cities?

4) Five youngsters entered a contest to guess how many marbles were in a bowl. Alice guessed 45, Betty guessed 39, Chuck guessed 49, Dan guessed 50, and Ed guessed 47. One was off by 6, one by 5, one by 2, and one by 4. One was right. Who was right?

5) A sheet of paper has statements numbered from 1 to 100. For each N, 1<=N<=100, Statement N says, "Exactly N of the statements in this sheet are false". Which statements are true?

6) You have normal 6-sided cube. I give you 6 different colors that you can paint each side of the cube with (one color to each side). How many different cubes can you make?

Optiver Math Test: Objective Questions

These are the questions asked in Optiver's Subjective Test. Do check Optiver's selection procedure for more information about shortlisting process of Optiver at IIT-Bombay.

1) What number comes next in this series: 1 11 21 1211 111221 312211 13112221 ?

• 12113331
• 1113213211
• 13221113
• 113211321

2) The following equation is wrong: 103 - 102 = 3. Move one numeral to make it correct. The numeral moved is ?

• 0
• 1
• 2
• 3

3) Imagine a 3*3*3 cube. How many cuts do we need to break it into 27 1*1*1 cubes ? (A cut may go through multiple pieces)

• 27
• 9
• 18
• 6

4) In a deck of 52 cards, what is the least number of cards you must take to be *guaranteed* at least one four-of-a-kind (eg: 4 queens) ?

• 4
• 16
• 28
• 40

5) Can you arrange the numerals 1 to 9 (1, 2, 3, 4, 5, 6, 7, 8 and 9) in a single fraction that equals 1/3 ? Example that doesn't work 7192/38456 = 0.187. The last 2 digits of the numerator of the above fraction are 

• 58
• 32
• 61
• 59

6) 5 pirates of different ages have a treasure of 50 gold coins. On their ship, they decide to split the coins using this scheme: The oldest pirate proposes how to share the coins, all of them will then vote for or against it. If 50% or more of the pirates vote for it, then the coins will be shared that way. Otherwise, the pirate proposing the scheme will be thrown overboard, and the process is repeated with the pirates that remain. Assuming that all 5 pirates are intelligent, rational, greedy and do not wish to die, how much will the 2nd youngest pirate get ?

• 97
• 98
• 0
• 20

I have posted the subjective section of the paper here.

Optiver Tests: Some Tips

Optiver is a market-making firm. Market-maker is basically a financial institution which quotes both a buy-price and a sell-price for different financial instruments. Thus, they are an important source of liquidity in the market and they make profit by the price differences in sell and buy quotes.

Optiver has been hiring a good number of students from IIT-Bombay for the last 2 years. It has become one of the most craved firms here at IIT-B, purely because of the job location, the lucrative package it offers, and also the kind of work it does. It has primarily hired for it's headquarters in Amsterdam, but it might hire for it's offices in Chicago and Sydney too.

Optiver has a very rigorous testing and interviewing process. It takes 3 written tests, and after every test it scalps approximately 50% of the students.

Shortlisting for the test is based on your Resume and CPI. Around 50% students are shortlisted for the test out of the total students who applied.

Test #1 : Speed Arithmetic (80 questions, 8 minutes, MCQ)

This is a pen-and-paper 8 minute arithmetic test! Yes you heard it right, it's only for 8 minutes. That's the beauty of it, in 8 minutes, it gets decided whether you are eligible for Optiver or not. It's a arithmetic speed-test and contains 80 simple arithmetic questions and you need to get around 60 right to clear this round. I recommend TraderTest for improving your chances.

1) The questions are very easy and based on + - * / only. Mostly integers.
2) Time taking questions are the ones involving fractions and mixed fractions
3) Since it's a pen and paper test, some time gets wasted on searching for the correct option and then  marking the option on the OMR sheet, so effectively you have less than 8 minutes.
4) Also, sometimes the options are not in their most simplified form eg. if the answer is 1/2, then you need to look for 3/6 or 6/12.
5) You get +1 for every correct answer and -2 for incorrect. You get -2 for skipping a question, Oops!
6) Cut-off score is around 60/80.


Test #2 : Sequences and Progression (25 questions, 30 minutes, MCQ)

After the 8-minute test around 50% of the students qualify for the 2nd test. For every question, you are given 6-7 numbers and then you have to recognize the next number in the sequence, you are given options to select from. The cut-off for this test is around 22/25, and there is no negative marking. Around 50% students clear this round.

You can practice from TraderTest, but it's not comprehensive. So you should also look at other resources on the web and in CAT study material.

Test #3 : Analytical Puzzles (Around 10 questions, 1 hour, Subjective)

The puzzles are math and number oriented. Practice a lot of puzzles from the web, some puzzles might get repeated. You need to write down the  correct approach to get full marks. Even if you don't know the right answer, writing some logical steps (although incomplete) might fetch you some marks.



Approximately half the students are eliminated after each round, so eventually only 1/8 of the total number of students make it to the final shortlist. At our time, around 35 students made it to the final shortlist out of 300 students who appeared for the test.

I have tried to give information as accurately as possible, but if you find any of the above incorrect, please bring it to my notice. I hope the above post helps you in your preparation :]