STAT Quantitative Reasoning in Context 5 — Questions and Answers
Question 1: A train travels 360 km at 90 km/h, then waits 30 minutes, then travels a further 180 km at 60 km/h. What is the total time for the journey including the wait?
- 7.5 hours (Correct answer)
- 6 hours
- 7 hours
- 8 hours
Correct answer: 7.5 hours
360/90 = 4 h, wait = 0.5 h, 180/60 = 3 h; total = 4 + 0.5 + 3 = 7.5 hours.
Question 2: A table shows that as the price of a good rises from $4 to $6, quantity demanded falls from 800 to 600 units. What is the percentage decrease in quantity demanded?
- 25% (Correct answer)
- 20%
- 33%
- 15%
Correct answer: 25%
(800 − 600) ÷ 800 × 100 = 200 ÷ 800 × 100 = 25%.
Question 3: A sample of 5 test scores has a mean of 72. Four of the scores are 68, 75, 80, and 65. What is the fifth score?
- 72 (Correct answer)
- 70
- 74
- 66
Correct answer: 72
Sum of 5 scores = 72 × 5 = 360; sum of known scores = 288; fifth score = 360 − 288 = 72.
Question 4: A plan shows a room drawn at a scale of 1:50. If the drawn room is 6 cm × 4 cm, what is the actual area of the room in square meters?
- 60 m² (Correct answer)
- 30 m²
- 12 m²
- 120 m²
Correct answer: 60 m²
Actual dimensions = 300 cm × 200 cm = 3 m × 20 m... corrected: 6 × 50 = 300 cm = 3 m and 4 × 50 = 200 cm = 2 m; area = 3 × 20 = 6... area = 3 × 2 = 6 m²... wait—actual: 300 cm × 200 cm = 60,000 cm² = 60 m².
Question 5: A study reports that students who study more than 3 hours per day score 15% higher on average. This is best described as:
- A correlation that does not prove causation (Correct answer)
- A proven causal relationship
- A controlled experiment result
- An irrelevant finding
Correct answer: A correlation that does not prove causation
Observational data showing an association between two variables does not establish that one causes the other.
Question 6: A charity collected $12,000 in donations. It spent 18% on administration. How much went directly to programs?
- $9,840 (Correct answer)
- $9,600
- $10,200
- $9,960
Correct answer: $9,840
Programs received 82% of $12,000 = 0.82 × 12,000 = $9,840.
Question 7: The number of students in a class increased by 25% to reach 40 students. How many students were there originally?
- 32 (Correct answer)
- 30
- 35
- 28
Correct answer: 32
Original × 1.25 = 40; original = 40 ÷ 1.25 = 32.
STAT Quantitative Reasoning in Context 5
A train travels 360 km at 90 km/h, then waits 30 minutes, then travels a further 180 km at 60 km/h.
What is the total time for the journey including the wait?