UCAT Decision Making Test #6 — Questions and Answers
Question 1: I pay out £1 to roll two dice. If exactly one die displays a five, I win £2. If exactly two dice produce a five, I win £10. <br> Should I anticipate making money if I play 36 games?
- Yes, because the potential prize is five times higher than the entry fee.
- Yes, because I can anticipate winning the same amount I paid to play.
- No, since only 1 in 6 people will receive a five.
- No, since on average I will lose more money than I spend on gambling. (Correct answer)
Correct answer: No, since on average I will lose more money than I spend on gambling.
To determine if playing 36 games is profitable, we calculate the expected value per game. There are 36 possible outcomes when rolling two dice. The probability of exactly one five is 10/36 (winning £2), and exactly two fives is 1/36 (winning £10). The expected winnings per game are (10/36 * £2) + (1/36 * £10) = £30/36 = £5/6. Since the cost to play is £1, the expected loss per game is £1 - £5/6 = £1/6. Therefore, over 36 games, an average loss of £6 is anticipated.
Question 2: Should election voting be done online, or if necessary, by mail, in order to cut expenses, enhance accuracy, and increase turnout? <br> Choose the one that you think best supports the claims below.
- Yes, compared to current counting techniques, electronic voting and counting would produce results more quickly and with a lower likelihood of error.
- The voting and counting mechanisms are now working well, therefore there is no need to change them. Instead, any innovations would be change for the sake of change.
- Yes, voting by mail or online would be more convenient for voters, which is likely to increase turnout in general.
- No, purchasing the necessary equipment would be expensive, using electronic voting would deter some voters, and there is a chance that hackers may tamper with the outcome. (Correct answer)
Correct answer: No, purchasing the necessary equipment would be expensive, using electronic voting would deter some voters, and there is a chance that hackers may tamper with the outcome.
The question asks for the best argument regarding online/mail voting to cut expenses, enhance accuracy, and increase turnout. Option D directly counters these claims by highlighting potential downsides. It points out that purchasing necessary equipment would be expensive, electronic voting might deter some voters, and there's a risk of hacking, directly addressing and refuting the proposed benefits of the change.
Question 3: Should the majority of students view university as a time to learn valuable transferrable skills and prepare for life rather than as offering vocational training for a specific job? <br> From the statements below, pick the one that makes the most sense.
- No, they already knew they wanted to become physicians and teachers; university is all about achieving certain professional goals.
- No, most people enroll in college because they have a specific future career in mind and are aware of why they want to study what they do.
- Yes, the majority of university courses are designed to prepare students for a variety of possible careers and lives rather than a single employment. (Correct answer)
- Yes, the majority of university students are adjusting to living independently and making their own decisions while living away from home for the first time.
Correct answer: Yes, the majority of university courses are designed to prepare students for a variety of possible careers and lives rather than a single employment.
The question asks whether university should be viewed as preparation for life and transferable skills, rather than specific vocational training. Option C supports this by stating that most university courses are designed to prepare students for a variety of possible careers and lives. This aligns with the idea of developing broad, adaptable skills and knowledge applicable to diverse paths, characteristic of a comprehensive university education.
Question 4: There are equal numbers of people with little feet, medium feet, and giant feet in the nation of Bipodia. <br> The population is equally split between those who have blue eyes, brown eyes, or green eyes. <br> Eye color and foot size are unrelated. <br> <br> Less than 35% of the 100 people drawn at random from Bipodia are predicted to have both blue eyes and small feet.
- No, one-third of people have blue eyes, and since foot size and eye color are unrelated, the total will be around 66.
- No, because foot size and eye color are unrelated and each fraction is one-third, the number will be around 44.
- Yes, one-third of people have blue eyes, and since foot size and eye color are unrelated, the percentage will be around 33.
- Yes, since foot size and eye color are unrelated and each fraction is one-third, the figure will be around 11. (Correct answer)
Correct answer: Yes, since foot size and eye color are unrelated and each fraction is one-third, the figure will be around 11.
If there are equal numbers of people with little, medium, and giant feet, then 1/3 of the population has small feet. Similarly, 1/3 of the population has blue eyes. Since eye color and foot size are unrelated, the probability of having both blue eyes and small feet is the product of their individual probabilities: (1/3) * (1/3) = 1/9. For a random sample of 100 people, (1/9) * 100 = 11.11, meaning around 11 people are predicted to have both blue eyes and small feet, which is less than 35%.
Question 5: Two goods were tested on the market by a corporation. <br> Users of the products left either favorable or negative feedback. <br> About 20 out of every 200 customers did not utilize Product A, and 10 out of every 180 people who did gave it poor reviews. <br> About 90% of the clients used Product B, and 25% of them left favorable reviews. <br> <br> Is Product A a better product to launch if we simply take into account the likelihood that buyers will utilize and like it?
- Yes, it is likely that Product A will sell more because there is a bigger chance that buyers will give it favorable reviews. (Correct answer)
- Yes, it is likely that Product A will sell more because there is a better chance that customers will utilize and like it.
- No, because Product B has a better probability of getting favorable feedback from clients, its sales will probably be larger.
- No, because Product B has a higher likelihood of being used by customers, its sales will probably be larger.
Correct answer: Yes, it is likely that Product A will sell more because there is a bigger chance that buyers will give it favorable reviews.
To compare the products, we calculate the likelihood of favorable reviews among those who used each product. For Product A, 180 customers used it (200 total - 20 did not use), and 170 gave favorable reviews (180 - 10 poor reviews), resulting in a 170/180 ≈ 94.4% favorable rate. For Product B, 25% of users left favorable reviews. Since Product A has a significantly higher chance of receiving favorable reviews (94.4% vs. 25%), it is the better product to launch based on this criterion.
Question 6: Should automobiles be equipped with a technology that caps the maximum speed they may go in order to decrease deadly traffic accidents? <br> Out all the arguments listed below, pick the most convincing one.
- Yes, driving at high speeds causes more pollution and requires more gasoline.
- Yes, fast drivers are responsible for a large number of fatalities. (Correct answer)
- No, drinking and driving results in more traffic fatalities than speeding.
- No, individuals should choose their own speed limits when driving.
Correct answer: Yes, fast drivers are responsible for a large number of fatalities.
The question asks whether speed-capping technology should be implemented to decrease deadly traffic accidents. Option B directly supports this by stating that 'fast drivers are responsible for a large number of fatalities.' This establishes a clear causal link between high speeds and deadly accidents, thereby providing a strong and relevant reason to implement a measure that limits speed.
Question 7: Field A has a 1 in 2 possibility of containing oil, and there is a 1 in 5 chance that any oil discovered there will be worth at least £1,000,000. <br> Field B has a 50% chance of holding oil, and a 2% chance that any oil found there will be worth less than £1,000,000. <br> Is it better to drill Field B as opposed to Field A based solely on the possibility of discovering oil and its price?
- Yes, there is a 98 percent chance that any oil discovered in Field B will have a value of at least £1,000,000. (Correct answer)
- No, there is a 30% higher chance of discovering oil in Field A and that it will be worth more than £1,000,000.
- No, Field A has a 50% higher chance of containing oil, and the price of any oil discovered there will be 80% higher.
- Yes, Field B has a 20% greater chance of yielding oil valued at $1,000,000 or more.
Correct answer: Yes, there is a 98 percent chance that any oil discovered in Field B will have a value of at least £1,000,000.
To compare drilling Field A versus Field B, we evaluate the probability of finding oil and its value. Both fields have a 50% chance of containing oil. For Field A, there's a 1 in 5 (20%) chance that any discovered oil will be worth at least £1,000,000. For Field B, there's a 2% chance that any discovered oil will be worth *less* than £1,000,000, meaning a 98% chance it will be worth at least £1,000,000. Therefore, Field B is better because if oil is found, it is much more likely to be of high value.
Question 8: 50 kids in a school were questioned about the subjects they took. <br> Geography and History were both studied by 10 pupils. <br> Geography was studied by 12 students but not History. <br> There were just as many people who did not study geography but did study history. <br> <br> How many pupils studied history overall?
- 10
- 15
- 30
- 24 (Correct answer)
Correct answer: 24
Based on the given information: 10 pupils studied both Geography and History. 12 students studied Geography but not History. The phrase 'just as many people who did not study geography but did study history' implies that 12 students also studied History but not Geography. Therefore, the total number of pupils who studied History overall is the sum of those who studied both (10) and those who studied only History (12), which equals 22. However, if the correct answer is 24, it implies that 14 students studied History only, which contradicts the 'just as many' statement referring to the 12 students who studied only Geography.
Question 9: Five racks are in a cabinet. On each of the five racks, Mara places one or two glasses. <br> How many racks did Mara place two cups on if there are eight cups in the entire cabinet?
- 2
- 3 (Correct answer)
- 5
- 6
Correct answer: 3
Let 'x' be the number of racks with two cups and 'y' be the number of racks with one cup. We know there are 5 racks in total, so x + y = 5. We also know there are 8 cups in total, so 2x + 1y = 8. Substituting y = 5 - x into the second equation gives 2x + (5 - x) = 8, which simplifies to x + 5 = 8. Solving for x, we find x = 3, meaning Mara placed two cups on 3 racks.
Question 10: 32 clients were given three different types of tiles from a retailer. The clients purchased one, two, or all three varieties of tiles. <br> Purchases of slate tiles totaled 16. <br> Only one buyer purchased marble and slate tiles. <br> Twelve buyers purchased cement and marble tiles. <br> Only six consumers purchased slate tiles. <br> All three tile kinds were purchased by 7 people. <br> Only three clients purchased marble tiles. <br> <br> How many clients solely purchased cement tiles?
- 3
- 4
- 5
- 8 (Correct answer)
Correct answer: 8
We can solve this using a Venn diagram approach. 7 clients purchased all three types. 1 client purchased only Marble and Slate. 5 clients purchased only Cement and Marble (12 total C&M - 7 all three). 6 clients purchased only Slate. From the total Slate (16), we find 2 clients purchased only Slate and Cement (16 - 6 - 1 - 7 = 2). 3 clients purchased only Marble. Summing these distinct groups (6+3+1+2+5+7 = 24), we subtract from the total clients (32) to find those who purchased only Cement: 32 - 24 = 8 clients.
Question 11: Should waste collectors forfeit their right to strike given that their job entails lowering potential health risks to the general public? <br> From the statements below, pick the one that makes the most sense.
- No, all employees, including public employees, have the right to strike if their wages and working conditions are poor, and it is the employer's duty to prevent health hazards. (Correct answer)
- No, garbage collection is a disagreeable and occasionally dangerous work, and it will be challenging to find enough garbage collectors until pay are raised.
- Yes, it simply costs taxpayers more when public employees like refuse collectors go on strike because councils are forced to spend more to recruit private collectors to remove waste.
- Yes, all strikes that endanger the health and safety of people who have already paid for services that are being withheld should be prohibited.
Correct answer: No, all employees, including public employees, have the right to strike if their wages and working conditions are poor, and it is the employer's duty to prevent health hazards.
The question asks whether waste collectors should forfeit their right to strike due to public health risks. Option A argues against forfeiting this right by asserting that all employees, including public sector workers, have fundamental rights to strike over poor working conditions. It places the responsibility for mitigating health hazards during a strike on the employer, rather than removing the employees' right to protest, upholding basic labor rights.
UCAT Decision Making Test #6
I pay out £1 to roll two dice.
If exactly one die displays a five, I win £2.
If exactly two dice produce a five, I win £10.
Should I anticipate making money if I play 36 games?