STAT - Special Tertiary Admissions Logical and Numerical Problem-Solving Questions and Answers — Questions and Answers
Question 1: A university regulation states: 'To be eligible for the Dean's List, a student must maintain a GPA of at least 3.5 AND have no failing grades.' Based only on this rule, which of the following statements is logically certain?
- Any student with a GPA of 3.8 and no failing grades will be on the Dean's List.
- A student who is not on the Dean's List must have a GPA below 3.5.
- Any student with a GPA of 3.6 but who has a failing grade cannot be on the Dean's List. (Correct answer)
- All students on the Dean's List have a GPA of exactly 3.5.
Correct answer: Any student with a GPA of 3.6 but who has a failing grade cannot be on the Dean's List.
The rule provides two necessary conditions to be eligible for the Dean's List. If a student fails to meet even one of these conditions (like having a failing grade), they are automatically disqualified, regardless of whether they meet the other condition (having a GPA above 3.5). Therefore, it is logically certain that a student with a failing grade cannot be on the list.
Question 2: In a group of 80 tourists, 50 speak Spanish, 35 speak French, and 20 speak both Spanish and French. How many tourists in the group speak neither Spanish nor French?
- 10
- 20
- 25
- 15 (Correct answer)
Correct answer: 15
To find the number who speak at least one language, we add the number who speak Spanish and the number who speak French, then subtract the number who speak both (to avoid double-counting). Total speaking at least one language = 50 (Spanish) + 35 (French) - 20 (Both) = 65. The number who speak neither is the total number of tourists minus this amount: 80 - 65 = 15.
Question 3: A company has 9 employees. Their annual salaries are: $50,000, $52,000, $52,000, $58,000, $65,000, $70,000, $71,000, $78,000, and $290,000. The company's management wants to present the most favorable 'average' salary in a recruitment brochure. Which measure of central tendency would they most likely use, and why?
- The median, because it is not affected by the unusually high salary.
- The mean, because the high salary of one employee inflates this value significantly. (Correct answer)
- The mode, because it represents the most common salary level.
- The range, because it shows the wide earning potential at the company.
Correct answer: The mean, because the high salary of one employee inflates this value significantly.
The mean (or arithmetic average) is calculated by summing all values and dividing by the number of values. A very high value (an outlier), like the $290,000 salary, will pull the mean upwards, making it significantly higher than the median ($65,000) or mode ($52,000). To present the most favorable (i.e., highest) figure, management would use the mean.
Question 4: A report concludes: 'The recent decline in the population of the native Silver Finch bird in Green Valley is due to the increased use of the new pesticide, Pest-Away, by local farmers. Since Pest-Away was introduced two years ago, the finch population has dropped by 30%.' Which of the following, if true, would most seriously weaken this argument?
- The Silver Finch population has also declined in a neighboring valley where Pest-Away is not used.
- Pest-Away is a government-approved pesticide certified as safe for birds when used as directed.
- Over the last two years, Green Valley has experienced a severe drought, which is known to decimate the insect populations that finches rely on for food. (Correct answer)
- The use of Pest-Away has led to a significant increase in crop yields for local farmers.
Correct answer: Over the last two years, Green Valley has experienced a severe drought, which is known to decimate the insect populations that finches rely on for food.
The argument presents a correlation (pesticide use and finch decline) and assumes a causal link. The strongest way to weaken a causal argument is to introduce a plausible alternative cause. A severe drought that destroys the finches' primary food source is a strong alternative explanation for the population decline, directly challenging the conclusion that the pesticide is the sole cause.
Question 5: Printer A can print a batch of documents in 30 minutes. Printer B can print the same batch in 60 minutes. If both printers start working together, how long will it take them to print one batch of documents?
- 45 minutes
- 90 minutes
- 20 minutes (Correct answer)
- 15 minutes
Correct answer: 20 minutes
We need to work with the rates of the printers. Printer A's rate is 1/30 of the job per minute. Printer B's rate is 1/60 of the job per minute. Their combined rate is the sum of their individual rates: 1/30 + 1/60 = 2/60 + 1/60 = 3/60 = 1/20. This means together they complete 1/20 of the job per minute. To find the total time, we take the reciprocal of the combined rate: 1 / (1/20) = 20 minutes.
Question 6: The table below shows international visitor arrivals (in millions) for two countries over three years, broken down by purpose of visit. | Year | Country | Holiday | Business | Visiting Family | Total | |---|---|---|---|---|---| | 2022 | Ausland | 1.2 M | 0.5 M | 0.8 M | 2.5 M | | 2022 | Borden | 2.1 M | 0.7 M | 0.2 M | 3.0 M | | 2023 | Ausland | 1.4 M | 0.6 M | 0.9 M | 2.9 M | | 2023 | Borden | 2.0 M | 0.8 M | 0.3 M | 3.1 M | | 2024 | Ausland | 1.8 M | 0.5 M | 1.0 M | 3.3 M | | 2024 | Borden | 2.2 M | 0.9 M | 0.3 M | 3.4 M | Which of the following statements is most accurately supported by the data in the table?
- From 2022 to 2024, the number of 'Holiday' visitors to Borden increased by more than 10%.
- In 2024, visitors for Business purposes made up a larger percentage of the total visitors for Ausland than for Borden.
- Ausland consistently had more visitors for the purpose of 'Visiting Family' than Borden had for 'Business'.
- The total number of visitors classified as 'Visiting Family' across both countries combined was highest in 2024. (Correct answer)
Correct answer: The total number of visitors classified as 'Visiting Family' across both countries combined was highest in 2024.
To verify this statement, we must sum the 'Visiting Family' numbers for both countries for each year. For 2022: 0.8M + 0.2M = 1.0M. For 2023: 0.9M + 0.3M = 1.2M. For 2024: 1.0M + 0.3M = 1.3M. Since 1.3M is the highest of the three totals, the statement is correct.
STAT - Special Tertiary Admissions Logical and Numerical Problem-Solving Questions and Answers
A university regulation states: 'To be eligible for the Dean's List, a student must maintain a GPA of at least 3.5 AND have no failing grades.' Based only on this rule, which of the following statements is logically certain?