Problem 1

You are an investment banker selling structured investments to high net worth individuals. Your customers are very rich, business savvy but not at all familiar with the field of mathematics. However, you have the daunting task of explaining to one of them the value of (pi, which is a greek alphabet and which also has a numerical value used very often in, amongst other disciplines, financial calculations). You will use the following statement to explain pi to your customer:

(a) pi is a number equal to 3.14159265.......
(b) if you take the perimeter of any circle in the world and divide it by its diameter       you will get the value of pi;
(c) If you invest value of pi in dollars at 3% rate of interest then after one year it       will become $3.23;
(d) pi is a mathematical constant that we use a lot in our calculations to price your       investments;

Problem 2

A glass is half filled with water. Which of the following statements is fuzzy?

(a) The glass is half full;
(b) The glass is half empty;
(c) The glass is both half full and half empty;
(d) The glass is either half full or half empty;

Problem 3

If GOOGLE = 2 and YAHOO = 2 then AOL = ?

(a) 3
(b) 0
(c) 1
(d) Cannot be determined;

Problem 4

John lives in Hong Kong, Simon lives in New York and Claire lives in Sydney . Each of these individuals travels to the other two destinations in such a way that they go to the other two destinations by taking the shortest possible route and by making consecutive journeys. For example, John will either travel to New York from Hong Kong and then from New York he will travel to Sydney and then back to Hong Kong or he will travel to Sydney and then to New York from Sydney and then come back to Hong Kong. And the same goes for the other two.

If all of them travel at the same time then what is the probability that none of these three cross each others path?

(a) 50%
(b) 16.67%
(c) 25%
(d) None of the above;

Problem 5

Tom Cruise is a movie star who lives in California. There is another Tom Cruise who is a plumber and he lives in Johannesburg. A third Tom Cruise is banker who lives in Tokyo. You are given the task by a credit reference agency to precisely and clearly identify the correct Tom Cruise with the correct location.

Which of the following logic statements would you prefer:

(a) IF Tom Cruise is a movie star THEN he lives in Californian ELSE IF he is a      plumber he lives in Johannesburg ELSE he lives in Tokyo
(b) IF Tom Cruise is a movie star THEN he lives in California ELSE he EITHER      lives in Tokyo OR in Johannesburg ;
(c) IF Tom Cruise is NOT a movie star THEN he lives in Tokyo or Johannesburg      ELSE he lives in California ;
(d) IF Tom Cruise is a plumber THEN he lives in Johannesburg AND IF he is a      movie star THEN he lives in California ELSE he lives in Tokyo ;

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