In a tournament, every rugby team except the winner is eliminated from the tournament after being defeated just once. Hence, the number of games required to find a tournament winner is going to be one less than the number of teams, or 22 in this case.
2. Suppose if there are 8 bags of wheat, 7 of which weigh the same amount. However, there is one that weighs less than the others. You are given a balance scale used for weighing. In less than three steps, figure out which bag weighs less than the rest?
Immediately, take any 2 of the bags and place them to the side. Weigh 3 of the remaining six bags against the other 3 bags. If these bags weigh the same, that means the bag that weighs less must be one of the two that you immediately placed to one side. If this is the case, weigh the 2 bags you placed to one side against each other to find out which one weighs less. You've now found in your bag.
However, upon weighing the sets of 3 bags against one another you find that one set weighs more than the other set, place one of the bags from the set of heavier bags aside and weigh the remaining two bags to find out which one is heavier. If they are of equal weight, the you know that the bag you place to one side is the bag you're looking for.
People coming into the subway tend to arrive at different times, so the flow of people down the escalators is a more even stream. Conversely, when people get off the subway they typically all arrive at the escalators at about the same time. Consequently, two escalators are need to handle people leaving the subway, where only one is required for people arriving.
4. You spend a third of all the money you have on a piano. Half of your remaining money you use to buy a piano chair. A quarter of the rest of your money you use to buy piano books. What proportion of you original money is remaining?
You spend a third of all the money you have on a piano, so you're left with two thirds (2/3). You spend half (1/2) of the remaining two thirds on a piano chair, which leaves you with just one third of what you started with (1/2x2/3=1/3).
You spend a quarter (1/4) of what you have remaining (1/3) on piano books, which leaves you with one twelth of the original (1/4x1/3=1/12).
5. Suppose You spend 21 dollars on vegetables at the store. You buy carrots, onions and celery. The celery cost half the cost of the onions. The onions cost have the cost of the carrots. How much did the onions cost?
Answering this problem just requires some simple algebra. If we assume the cost of celery = x, then the cost of onions = 2x, and cost of the carrots is 4x, such that the total cost of all vegetables = x + 2x + 4x = 7x = 21 dollars. Consequently, x = 3 dollars. Hence, the onions cost 6 dollars.
This section evaluates potential solutions for the identified key problems. Often there is more than one solution, so it is useful to evaluate each solution in terms of its advantages and disadvantages. This will also assist in determining your recommendations. Things that may need to be considered are:
Integrating relevant theory into your case study answer is vital. This allows you to demonstrate how theory relates to the actual issues / problems found in the case study, as well as demonstrate your understanding of your course content.
Mind maps can be a useful strategy to summarize / organize problems and to show their relationships to each other.
Relating the identified issues / or problems to theory is vital when answering case studies. This is where you demonstrate your knowledge of the theory in your course and your ability to relate it to practical situations. Use your readings to select appropriate theories to match the identified problems.
Identifying the major problems and their causes at this stage is vital to identify appropriate solutions later. Re-read the case study and summarize or list the issues and / or problems in your own words. Make sure you:
❅ Sort the major problems from the minor problems
❅ Identify evidence from the case study which relates to each of the problems
❅ Identify underlying causes of the problems.
A useful strategy is to represent the problems and their relationships as a mind map.