Decision Making

In a council, there are Elders, Advisors, and Messengers. All Elders are Advisors, but not all Advisors are Elders. No Messenger is an Elder, and no Messenger can become an Elder. Some Advisors are also Messengers, but no Elder is a Messenger. If someone is not a Messenger, they must be either an Elder or an Advisor, but not both.

All smart students have a pen license. A pen license indicates a devotion of hours in utilising a pen, however it does not indicate that the writing is legible. Some people are students.

Some girls enjoy playing sports, and some boys do not enjoy playing sports. If a boy enjoys playing sports, then he must also enjoy watching sports. However, not all girls that enjoy playing sports enjoy watching sports. This person either enjoys playing sports, or enjoys watching sports.

In a university, every course that includes fieldwork requires students to complete a safety training module. Some courses include laboratory work but no fieldwork. A few courses require both fieldwork and laboratory work. If a student takes a course with no fieldwork, safety training is optional.

In a national art competition, each participant must submit a painting or a sculpture, but not both. Some participants choose to submit abstract pieces, while others submit realistic pieces. Every sculpture submitted must include at least one metallic element. Participants who submit abstract paintings are not required to use any specific materials.

Joseph and Anna had their first child, Emily, in 2016. They later adopted 4-year-old Rainer in 2020. Isabella was born to Martin and Sarah, and they celebrated her 6th birthday in 2024. Martin and Sarah have another child, Kody, who is older than Rainer. Which of the following must be true?

Which of these statements MUST be true?

Four new employees—Alice, Bob, Cora, and Daniel—each ordered a unique lunch (salad, sandwich, soup, or pasta) and a unique drink (water, soda, juice, or coffee) from the cafeteria. No two employees share the same lunch or the same drink.

Bob did not order salad, but he did order water to drink.

The sandwich order was not paired with soda.

Either Cora or Daniel ordered soup.

Alice does not drink soda or juice.

The salad came paired with juice.

Which of the following is MOST LIKELY to be true?

Four students—Elena, Farhan, Gina, and Hasan—each attend a different club meeting (Debate, Drama, Film, or Chess) on a different day of the week (Friday, Saturday, Sunday, or Monday). Each student goes to exactly one club, and no two students attend on the same day.

Elena must attend on a day earlier than the day when the Drama club meets.

Hasan attends on a later day than the Film club meets.

The Chess meeting is not on Saturday, and is not run by Hasan.

Farhan hates traveling on Sundays, so he never has a meeting on Sunday.

Gina attends Drama.

Which of the following must be true?

A family of five – consisting of a mother, father and three sons – decide to get a dog, but only if each individual has a specific job to make sure everything runs smoothly.

An adult must take the dog to the groomer every couple of weeks. The youngest son is too young to walk the dog, so he needs to make sure the water bowl is always topped up. One of the children needs to feed the dog twice a day. The mother offers to brush the dog once a day.

Which of the following must be true?

Should governments provide free university education to all students?

Should internet service providers be allowed to censor certain websites at their own discretion to charge extra for premium unrestricted access?

Should allowing children under the age of 15 to play any video games be made illegal in order to promote healthy brain development?

Should the selective breeding of brachycephalic dogs (pugs, boxers, bulldogs, etc.) be banned to reduce the number of health problems these breeds are now prone to?

Should gum be allowed to be chewed in school to alleviate student stress and improve grades?

The results of a poll to determine the favourite colours of men and women are presented in the pie charts below. Each sector of the pie represents the percentage of that sex that identified that colour as their favourite. Decide whether the following conclusions follow:

The spider-plot depicts the percentage of particular pollutants produced during the manufacturing and operation of various power generating technologies. The percentage of the total emissions from the respective technology, not the whole. Decide whether the following conclusions follow:

A milkman is taking ten full fat milk cartons, five semi-skimmed milk cartons and three skimmed milk cartons to his normal delivery area. On the way, four of the milk cartons fall off the milk float and are lost.

Four medicines have been mistakenly labelled and are on the counter in the medicine room Luckily each medicine, A, B, C and D are in different forms, there is a tablet, a powder, a liquid and an inhaler. You also know that the dosages are all different, and they are: 10mg, 30mg, 60mg, 120mg (in no particular order).

• Medicine B is not an inhaler.
• Medicine D is a tablet.
• The dosage of Medicine D is less than, but not half of the dosage of Medicine A.
• Medicine C is a powder but its dosage is not the largest.

The local bakery sold 100 doughnuts (A), half regular and half sugar-free. Out of the sugar-free ones, 10 had cocoa filling and 10 had cocoa & vanilla. Another 10 had fruit glaze and vanilla filling and the rest were all simple doughnuts with fruit glaze. +

How many sugar-free doughnuts with fruit glaze were baked?

A student is going through a hospital and taking a tally of patients and the speciality under which they are being treated. Each patient can only be under one specialty. The student finds that 25% are under orthopaedics; 21% are under cardiology; 20% are under respiratory; 12% are under gastroenterology; the remaining patients the student classes as other.

Which of the following is definitely true according to this information?

56 medical students are arriving at their new hospital for their next rotations in acute care. 20 are assigned to the Emergency Department. 26 are assigned to anaesthetics, of which 8 are focused on anaesthetics in the Emergency Department. 30 are assigned to surgery, of which 10 are also on anaesthetics, and 2 are on surgery and ED. There are no students assigned to the Emergency Department, surgery and anaesthetics.

Which of the following options represents this?

First graders took a trip to the stationary store. The entire class bought 13 books, 7 pens, and 9 crayons. One of the kids bought 3 books and 3 pens, another bought 2 pens and 2 crayons. There is 1 kid who only bought a pen.

How many kids bought 1 of each item?

There are 32 people on the bus, and they are either adults or children. 11 of the 17 children are female. There are 2 more females than males.

What is the number of female adults on the bus?

Should fast food restaurants be banned from selling ‘junk food’ to children during their lunch hour at school?

Should nuclear power plants be eliminated to prevent radiation leaks caused by reactor meltdowns?

Should commercial egg sales be banned to prevent the animal abuse of many chicken factory farming operations?

Kaedi is drawing marbles from a bag. There are 15 pink marbles, 15 blue marbles. She bet her friend Kendall that she will first draw a pink marble and then draw a blue marble. Neither marble will be placed back into the bag after being drawn.

Kaedi figures she has at least a 1/2 chance of winning the bet, is she correct?

In order to win a large prize at a carnival Amelia must guess what 4-digit number a random number generator will create. Amelia knows the first digit is always a 1, the second digit can only be either 7 or 0, the third digit can only be a 1, 3, or 9, while the fourth digit can be any number. Amelia thinks she has at least a 1 in 100 chance.

Is Amelia correct in thinking she has at least a 1% chance of winning?

Two friends were playing a card game using a standard deck of 52 cards (13 cards of each suit). Ethan has a 10 and an 8, Mason has a 9. Mason is about to draw a second card, in order to win it must be a 10, Jack, Queen, King, or Ace.

Does Mason have at least a 40% chance of winning?

In a randomised drug trial, 50% of the participants were given the trialled drug and the remaining
50% were given a placebo. However, 60% of all of the participants in the trial did not see an improvement in their symptoms.

Which of the following must be true?

There are several major exceptions on tuition fees. In many European countries, it is possible to study without tuition fees. Public universities in Nordic countries were entirely without tuition fees until around 2005. Denmark, Sweden and Finland then moved to put in place tuition fees for foreign students. Citizens of EU and EEA member states and citizens from Switzerland remain exempted from tuition fees, and the amounts of public grants granted to promising foreign students were increased to offset some of the impact.

Superficially, all governments have an official or ideal form. The United States is a constitutional republic, while the former Soviet Union was a socialist republic. However self-identification is not objective, and as Kopstein and Lichbach argue, defining regimes can be tricky. For example, Voltaire argued that “the Holy Roman Empire is neither Holy, nor Roman, nor an Empire”.

Democracy is a system of government where the citizens exercise power by voting. In a direct democracy, the citizens as a whole form a governing body and vote directly on each issue. In a representative democracy the citizens elect representatives from among themselves. These representatives meet to form a governing body. In a constitutional democracy the powers of the majority are exercised within the framework of a representative democracy, but the constitution limits the majority and protects the minority, usually through the enjoyment by all of certain individual rights, e.g. freedom of speech, or freedom of association.

A republic is a form of government in which the country is considered a “public matter”, not the private concern or property of the rulers, and where offices of states are subsequently directly or indirectly elected or appointed rather than inherited. The people, or some significant portion of them, have supreme control over the government and where offices of state are elected or chosen by elected people. A common simplified definition of a republic is a government where the head of state is not a monarch. Philosopher Montesquieu included both democracies, where all the people have a share in rule, and aristocracies or oligarchies, where only some of the people rule, as republican forms of government.

Hydroelectricity is the application of hydropower to generate electricity. It is the primary use of hydropower today. Hydroelectric power plants can include a reservoir (generally created by a dam) to exploit the energy of falling water, or can use the kinetic energy of water as in run-of-the-river hydroelectricity. Hydroelectric plants can vary in size from small community sized plants (micro hydro) to very large plants supplying power to a whole country. As of 2019, the five largest power stations in the world are conventional hydroelectric power stations with dams.