Quantitative Reasoning in Context Flashcards

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?

Answer: 7.5 hours

360/90 = 4 h, wait = 0.5 h, 180/60 = 3 h; total = 4 + 0.5 + 3 = 7.5 hours.

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?

Answer: 25%

(800 − 600) ÷ 800 × 100 = 200 ÷ 800 × 100 = 25%.

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?

Answer: 72

Sum of 5 scores = 72 × 5 = 360; sum of known scores = 288; fifth score = 360 − 288 = 72.

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?

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.

A study reports that students who study more than 3 hours per day score 15% higher on average. This is best described as:

Answer: A correlation that does not prove causation

Observational data showing an association between two variables does not establish that one causes the other.

A charity collected $12,000 in donations. It spent 18% on administration. How much went directly to programs?

Answer: $9,840

Programs received 82% of $12,000 = 0.82 × 12,000 = $9,840.

The number of students in a class increased by 25% to reach 40 students. How many students were there originally?

Answer: 32

Original × 1.25 = 40; original = 40 ÷ 1.25 = 32.