My Math Forum Interview questions

 Algebra Pre-Algebra and Basic Algebra Math Forum

February 16th, 2012, 10:33 AM   #1
Senior Member

Joined: Jan 2010

Posts: 205
Thanks: 0

Interview questions

These came up for a job interview and they had to be answered relatively quickly (most of them should be answered within one minute):

Quote:
 1) Prove the Law of Cosines (For any triangle: a^2=b^2 + c^2 - 2abcos(theta)) 2) How much would you pay to play this game: You roll a die and are paid whatever amount comes up on the die. You are allowed to roll again if the number is 4 or above. You do not get to roll again if the number is 3 or below. 3) Give an algorithm to test if a number is prime in time better than O(n) 4) If you pick two numbers between 0 and 1, what is the probability that the product of those two numbers will be greater than .5? 5) If you have a fair coin and want to simulate an event that has probability 1/3 and probability 2/3, how can you do that? 6) You have two robots placed randomly on the number line. When they land, they place a marker. You are to program the robots so that they meet, and you are given the following 3 commands: Go left, go right, or if you are on a marker, change strategy. Specify the two strategies so that the robots eventually meet. 7) Give an algorithm to reverse the order of the letters of each word in a sentence. Do not change the order of the words. For instance if your sentence is "I like cookies", this algorithm should return "I ekil seikooc" 8) What is happening in Greece? What countries are in trouble? Why is the Republic of Ireland in trouble? Why are the rest of the countries in trouble? Why do all the European banks have so much Greek debt? 9) There is a 5 game series, and you would like to bet on the outcome of the series. You have 100 dollars. If your team wins, you want to get 200 dollars at the end of the series, if they lose you want 0. The problem is that you can only bet on each individual game. How do you bet on each game? 10) You have a 6 barrel revolver with 2 bullets in it, placed side by side. You are going to play Russian Roulette. You play once and don't die. Do you spin the barrel again and then pull the trigger, or do you just pull the trigger? 11) You have two options. One has a strike price of 1300, one has a strike price of 1400. Which is cheaper and why? 12) What parameters would you need to price an option?
I know a few of the questions aren't applicable to mathematics, but I included them just for curiosity's sake for those who want to know what they were.

February 16th, 2012, 12:50 PM   #2
Math Team

Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 407

Re: Interview questions

Hello, daigo!

A job interview for what profession? . . . NASA consultat?
There is a typo in #1 . . . it should have $2bc\cos A$

Quote:
 $\text{1) Prove the Law of Cosines (for any triangle): }\:a^2 \:=\:b^2\,+\,c^2\,-\,2bc\cos A$

I can do this . . . but only because I taught Trigonometry for years and years.

The average job applicant doesn't have a prayer!

Quote:
 $\text{5) If you have a fair coin and want to simulate an event that}$ $\text{has probability }\frac{1}{3}\text{ and probability }\frac{2}{3}.\;\;\text{How can you do that?}$

Toss the coin twice.
There are four equally likely outcomes:[color=beige] .[/color]$HH,\:HT,\:TH,\:TT$

$\text{Disregard }TT.$

$\text{And we will use: }\:\underbrace{HH}_{P(A)},\:\underbrace{HT,\:TH}_{ P(A'}" />

February 17th, 2012, 09:25 AM   #3
Math Team

Joined: Oct 2011

Posts: 10,485
Thanks: 693

Re: Interview questions

Quote:
 Originally Posted by daigo 7) Give an algorithm to reverse the order of the letters of each word in a sentence. Do not change the order of the words. For instance if your sentence is "I like cookies", this algorithm should return "I ekil seikooc"
What kind of cookies? Chocolate with raisins?

algorithm (?æl???r?ð?m)
maths, a recursive procedure whereby an infinite sequence of terms can be generated

Hmmm....

Read 1st word : A$= 1st word Dowhile A$<>"blank"
x = length(A$) For n = x to 1 step -1 Print A$(pos(n))
Next n
Print " " (leave space between words!)
Read next word : A\$ = next word

After I leave, my application "accidentally" falls in the waste paper basket

 Tags interview, questions

### jobs that involve advanced math

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post eChung00 Advanced Statistics 1 March 6th, 2013 02:30 AM r-soy Calculus 4 March 2nd, 2013 03:46 PM Telpjmal New Users 5 May 22nd, 2012 12:22 PM simon76 Math Events 0 March 3rd, 2012 10:15 PM beast1934 Calculus 1 June 16th, 2009 07:20 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top