Saturday, April 16, 2011

Saturday April 16, 2011

This is federal election time in Canada as well as budget talk in the US. Questions are based on those!

  • The total US debt  as of March 25, 2011 is  14.26 trillion dollars. How much is 1 trillion? (Just to put this number in perspective - total public parking spaces (metered/road) etc. in San Francisco is about 500,000. Average cost of a car in that area is about $30,000. Compare the debt in terms of some quantity you can imagine.
  • Here is an alternate way to understand this figure. The population of US is approx. 311,000,000. Whats the debt per person then? per family? What will a family do if they are in such a debt?
  • Canada's debt is approximately 540 billion dollars, and population is 33,739,000. Compare the debt per person and per family v/s US. Growing economy like India has a debt of approximately 750 billion $s. Population is 1.2 billion. 
  • What is debt? This is essentially what govt. owns to people (shares/bonds...). Usually it is seen in comparison to GDP, gross domestic production. This is the market value of all the goods and services produced within a country in one year.  Canada's GDP is about 1.6 trillion $, debt around 540 billion $. US GDP is 14.6 trillion and debt 14 trillion. (How can Prime Minister/President reduce debt and increase GDP - whats a healthy economy?) 
  • During the federal election in Canada, it is claimed that the cost of election is $300 million dollars. Calculate whats the cost of election per household in Canada? We are having almost one election/year - as opposed to one in 5 years.
  • In 2008, in Canadian elections, there were approximately 23,000,000 voters on list and only 14,000,000 voted. The distribution of votes in this election between main parties (Conservatives, Liberal, Bloc, NDP, Green) were  (38%,27%,10%,18%,7%) and the number of seats in the parliament were (143, 77, 49, 37, 0), respectively.  What do these numbers mean? Does parliament reflect the % of votes? Can you think of a better mechanism?
  • If you hear the results on May 2, after the polls close, you will see many types of graphs, analysis, trends, ups and downs etc.   Can you think of drawing a line graph whose slopes are 1, 0, -1, 2, 3, -2, -3.  What linear equations these graphs satisfy assuming that they pass through the origin.  
  • If I have a line segment, lets say originating at (0,2) and ending at (4,13), then I can measure its length by actually drawing it and then use a ruler. Can I do in some other way as well?  In general if the coordinate of the endpoints are (x1,y1) and (x2,y2), what is its length?

Sunday, April 10, 2011

Sunday April 10, 2011

  1. On the Boxing Day (26th Dec.), stores need to come up with curious ways to give discounts to attract customer. Here is an interesting one - the store is offering a discount of  an additional 10% every hour  -  what will be the price of an item worth $100, at 9AM, 10AM, 11AM, ..., 5PM. Think of - it the discount is on the original price or the last listed price. Since you know that there are limited quantities of each of the items,  how should you approach?  If all the customers can cooperate what could be your strategy - what if they do not want to cooperate at all?
  2. In 10 seconds, the distance that a cheetah, cyclist, and an Olympian  runner can cover are respectively 300m, 160m and 110m. What is their speed? How much they would have covered in 8 seconds or 12 seconds - assuming a constant speed? Whats the best way to find out the distance for any given time duration?
  3. A right angled triangle with base 4mts, aligned to x-axis, has an area of 6m^2. What is the slope of its hypotenuse? 
  4. Whats is the slope of a Standard Staircase?  (By the way the code for staircases is 7-11, i.e. 7 inch rise for each 11inch.)  Typically the 1st floor ceiling is about 9ft,  how many steps will it require?  Whats the linear distance one needs to reach 9ft, if each step is 11inch deep. Many places steps are made in L, U or semicircular shape - any idea why one builds these shapes?
  5.  Last few questions dealt with the slope of a straight line - which is defined to be `rise' over `run'. What can one say about slope of a curve? or a surface? How will one go about computing slope of a curve?
  6. Each electron has a charge of  1.6 * 10^-19 Coulomb.  How many electrons you need to make a charge of 1 Coulomb?
  7. Current in electrical circuits means how much charge passes through a conductor in 1 second. For example, current of 1 Ampere means a charge of 1 Coulomb has gone through the conductor in 1 second - think of how many electrons have moved through - traffic jams?   If the fuse in the house has a rating of 10 A, then how much charge has gone through the fuse in 1 second? How many electrons? 
  8. My house has an electric panel and it is rated as 100 Amp. What does that mean? Lets take any household appliance - for example a computer - and lets look at its ratings? Can we figure out how many computers can we run on a 100 Amp circuit, where we have 110 Volts. What about some more heavy duty appliance like - drier or stove. For example stove are rated for 20Amps.

Sunday, April 3, 2011

Sunday April 3, 2011

  •  The above graph  (taken from a Forex Blog) shows the trend of CAD/USD loonie over last  5 years. Any conclusions can you draw?
  • This is year of India in Canada. Indian Government decided to take up a survey to see how are Indian's performing outside India. They needed to compare Indians living in `similar' type of countries - for example US, Canada, UK and Australia. What should be a good hypothesis to test? What kind of primary/secondary data can be used? What kind of conclusions can be drawn? Is there any point of doing this kind of study?
  • Mr. Ad. needs to form a team of 30 players who will participate in several of summer sports (sort of mini summer olympics) where the sports include running, field hockey, tennis, soccer, jumping, swimming, etc. What selection criteria should he use (name at least 5).  Design some hypothesis to test whether the selection criteria leads to medals. What kind of data primary or secondary can be used to verify his hypothesis.
  • Here is a chart showing  (taken from here) Speed v/s Safe stopping distance in icy v/s normal conditions. Why do you think its not a straight line curve?
  • This web-site lists some of the super cars, their price and the time (in seconds) it takes them to reach the speed of 100Km/hr.  For example, 2005 Ferrari FXX reaches that speed in 2.5 secs, and it costs $1.5 million.  What kind of plot do you expect in terms of price v/s time it takes to attain 100Km/hr. (For example my car takes 7.4 secs - though I never tried that).
  • What kind of distance-time graph you will expect when you hit a Home run in Baseball - the launch of a satellite - a train entering a station to stop - tiger chasing its kill - in general a typical commute from home to office  (In distance time graph, you will plot the distance of the ball (or an object) from its original position as time increases).
  • How many odd 1-digit, 2-digit, 3-digit, 7-digit numbers can be formed using the digits 1,2,3,4,5,6,7, if each number consists of distinct digits (e.g. 223 is not valid!).
  • This one is based on Zero Knowledge Proofs - its an interesting  concept.  See wikipedia entry on this (this picture is from there) Idea is pretty simple. Both of these persons don't trust each other. Person standing outside the cave (call him Bob), needs to know the number-key of  the door which is at the far end of the cave. Person standing in the cave (call her Alice) claims that she knows the number key, and is willing to give that key for $100. Bob, can gamble, and pay Alice $100, and hope that she is telling the truth. But she may not!  How can Alice convince Bob that she knows the key, without revealing the key, especially before Bob pays her $100! This kind of technique is used, for example the password you have on your bank card.