Pre-Interview
(Ten minutes)
1) Mental Math: One million minus one hundred eleven.
2) Mental Math: Fifty-four percent of one hundred ten.
3) Game: With one die, suppose in a round, you earn the amount of dollars equal to
the value of the upwards face of the die. (eg. you earn $6 if you roll a six.) Now also
suppose after your first roll, you are given the opportunity to cancel your first and roll
again, taking that value as the final value. What should your strategy be?
4) What's the closest integer to the square root of 1420.
5) You and a roommate are hosting a party. You invite 10 other pairs of roommates.
During the party you poll everyone at the party (excluding yourself) and ask how
many hands each person shook. Two conditions:
a) Each person did not shake his roommate's hand.
b) Each person shook a different number of hands.
Question: How many hands did you roommate shake?
6) a) You roll a die, and are given an amount in dollar equal to the number on the die.
What would you pay to play this game if you played it a lot of times?
b) now say that when you roll the die, you're allowed to either take the money that
you'd get with the roll, or roll a second time; if you roll a second time, you're
obligated to take the number of dollars that you get with the second roll. Now what
is the worth of the game?
c) Same thing as above, except you have an option to play the game a third time.
Interview
(Thirty minutes)
1) Suppose you are given the opportunity to bid for a treasure chest, which you know
with 100% confidence to be priced anywhere between $0-$1000. If you bid equal to
or above the price, you win the treasure chest (at the cost of your bid). If you bid
below the price, you do not earn the treasure chest. Now, also suppose you have a
friend who is willing to buy the treasure chest from you for one and a half times the
price of the treasure chest (should you obtain the chest). What should your bid be?
2) In Baseball, the batting average is the number of hits over the number of at bats.
Player A has a greater batting average than Player B in the first half of the season and
the second half of the season. Is it possible that Player B would have a higher batting
average for the entire season?
3) How much calories does a Big Mac have? Would you bet $1 on it? How about $10?
4) How many tons does the ocean weigh?
5) How much would you be willing to bet on it being within 25% of that at even
odds?
6) A company has a value V which is uniformly distributed between 0 and 1. you are
planning to place a bid B for the company. If B is smaller than V, then your bid loses
and you get nothing; if B is larger than V, you get to purchase the company at price B,
and the company will end up being worth 1.5 * V. What price B should you bid to
maximize your profit?
7) On a sheet of paper, you have 100 statements written down. the first says, "at
most 0 of these 100 statements are true." the second says, "at most 1 of these 100
statements are true." ... the nth says, "at most (n-1) of these 100 statements are
true. ... the 100th says, "at most 99 of these statements are true." how many of the
statements are true?
8) You have two decks of cards: one has 13 reds and 13 blacks, and the other has 26
reds and 26 blacks. We play a game in which you select one of the two decks, and
pick two cards from it; you win the game if you select two black cards. Which deck
should you select to maximize your chances of winning? Try to do this problem in
your head, without writing any calculations down.
9) You have a deck of 52 cards, and you keep taking pairs of cards out of the deck. if a
pair of cards are both red, then you win that pair; if a pair of cards are both black,
then I win that pair; if a pair of cards has one red and one black, then it's discarded.
If, after going through the whole deck, you have more pairs than I do, then you win
$1, and if I have more pairs than you do, I win $1. What is the value of this game in
the long run?
