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.