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.
Understanding the background issues helps to understand the context of the case study. Read the case study to gain an overview and ask and answer the following questions as you read.
What background facts influence the current problems?
What are the constraints or obstacles of the situation?
A case study is not just the recount of the issues and problems, it is also the detailing of solutions and recommendations, eg an action plan, to fix the problems. Case studies are generally presented in report format using headings and subheadings, but check with your teacher / lecturer for prescribed formats.
☛ Identification of issues & problems
Describe the actions you took:
why did you choose these actions?
What were the results you expected to achieve?
Describe how you organized ideas into process flow and common theme and the way you monitor result. Don't forget the risk management factors.
Explain the factors you took for making a decision:
How did you get to the root cause of the problem?
How did you identify the likely causes of problem?
How did you generate a number of possible solutions?
Tell about how you collected information for analyzing data: the process you utilized for extracting maximum information from the facts.
Describe the problem in the workplace. What is involved in making it a problem?
In a knockout competition, every team except the winner is defeated once and once only, so the number of matches is one less than the number of teams in this case 23-1 = 22.
Put 2 bags to the side. Weight 3 of the remaining bags against the other 3 remaining. If they weigh the same then weigh the 2 bags that you put aside to find out which of them is heavier. If, however, one of the sets of 3 bags was heavier, put one of the bags from the heavier set aside. Weigh the remaining two bags from the set to find out which one is heavier. If they are equal then you know that it is the 1 bag that you put aside.
20. Suppose if there are three boxes, one contains only apples, one contains only oranges, and one contains both apples and oranges. The boxes have been incorrectly labeled such that no label identifies the actual contents of the box it labels. Opening just one box, and without looking in the box, you take out one piece of fruit. By looking at the fruit, Tell me how can you immediately label all of the boxes correctly?
Open the box that is labeled "Apples and Oranges".
You know that since none of the labels are correct, the box must either contain only apples, or only oranges.
Suppose that you remove an apple from that box. Therefore, that box must be the "Apples Only" box.
One of the two remaining boxes must be the "Oranges Only" box. However, one is labeled "Apples Only", and the other is labeled "Oranges Only". Therefore, the one labeled "Apples Only" is the box that contains only oranges, and the box labeled "Oranges Only" is the box that contains both kinds of fruit.
People leave trains packed in a group, so arrive at the escalators at the same time, but tend to go down to the trains in a more even stream.
After spending one third of my money on the guitar I have two thirds left. I spend half of this on a microphone, so this is again one third. I then have one third of my original money remaining. I spend one quarter of this on the kazoo. One quarter of one third is one twelfth. I thus have three quarters of one third of my money remaining. Three quarters of one third is one quarter remaining. (1/3 = 4/12. 4/12 - 1/12 = 3/12. 3/12 = 1/4)
Round covers can never be dropped down the hole, but square ones can if you turn them diagonally to the hole.
24. You spend 21 Euros on meat in a supermarket. You buy a turkey, a chicken and a salmon. The salmon costs half the cost of the turkey and the chicken costs half as much as the salmon. How much did the turkey cost?
Use simple algebra. Say cost of chicken = x, then cost of salmon is 2x and cost of turkey is 4x
Therefore total cost = x + 2x + 4x = 7x
7x = 21 Euros
Therefore x = 3 Euros
Turkey costs 4x which is 12 Euros
25. Suppose A sheep farmer has to get to his herd of sheep quickly as he has been told they are being attacked by a dog. His sheep are on the other side of a steep hill. He can run over the hill (2 miles) at 3 miles an hour, or take his tractor via an old dirt track which is 5 miles at an average of 6 miles an hour or he can drive his Land Rover along a very narrow winding road but this is 12 miles and he can only go at 16 miles an hour on average?
Running 2 miles at 3 mph takes 40 minutes
Driving the tractor for 5 miles at 6 mph takes 50 minutes
Driving the Land Rover for 12 miles at 16 mph takes 45 minutes
Therefore he should run.
The answer is not zero degrees as you might at first think. The minute hand will be at 15 minutes (90 degrees clockwise from vertical) but the hour hand will have progressed to one quarter of the distance between 3 pm and 4 pm.
Each hour represents 30 degrees (360 / 12), so one quarter of an hour equals 7.5 degrees, so the minute hand will be at 97.5 degrees: a 7.5 degree difference between the hands.