TMU Problem Solving 2 — Questions and Answers
Question 1: A store sells apples for $0.75 each and oranges for $1.25 each. If Maria spends exactly $10.00 buying a total of 10 pieces of fruit, how many apples did she buy?
- 4
- 5 (Correct answer)
- 6
- 8
Correct answer: 5
Let a = apples and o = oranges; a + o = 10 and 0.75a + 1.25o = 10, solving gives a = 5.
Question 2: A rectangular garden has a perimeter of 48 m. If its length is twice its width, what is its area?
- 64 m²
- 128 m² (Correct answer)
- 96 m²
- 144 m²
Correct answer: 128 m²
Width = 8 m, length = 16 m, area = 8 × 16 = 128 m².
Question 3: Which strategy is most effective when a problem has many possible solutions and no obvious starting point?
- Work backward from the goal
- Guess and check systematically
- Draw a diagram
- Make an organized list of cases (Correct answer)
Correct answer: Make an organized list of cases
Creating an organized list ensures all possibilities are examined without missing or repeating cases.
Question 4: A clock shows 3:15. What is the angle between the hour and minute hands?
- 0°
- 7.5° (Correct answer)
- 22.5°
- 45°
Correct answer: 7.5°
At 3:15, the minute hand is at 90° and the hour hand is at 97.5° (3×30 + 15×0.5), giving a difference of 7.5°.
Question 5: If the pattern 2, 6, 12, 20, 30 continues, what is the next term?
- 40
- 42 (Correct answer)
- 44
- 48
Correct answer: 42
Differences are 4, 6, 8, 10, 12 — the next term is 30 + 12 = 42.
Question 6: A train travels from City A to City B at 60 km/h and returns at 40 km/h. What is its average speed for the entire trip?
- 48 km/h (Correct answer)
- 50 km/h
- 52 km/h
- 54 km/h
Correct answer: 48 km/h
Average speed = 2(60)(40)/(60+40) = 4800/100 = 48 km/h using the harmonic mean formula.
Question 7: A container holds 24 liters. You have a 5-liter jug and a 7-liter jug with no markings. How can you measure exactly 6 liters?
- Fill the 7-liter, pour into 5-liter, leaving 2 liters — repeat three times (Correct answer)
- Fill the 5-liter, pour into 7-liter twice — leaving 3 liters each time
- Fill the 7-liter twice and subtract 8 liters
- Fill the 5-liter jug and add one full 7-liter jug
Correct answer: Fill the 7-liter, pour into 5-liter, leaving 2 liters — repeat three times
Filling the 7-liter and pouring off 5-liter three times gives 3×2 = 6 liters after combining two partial fills.
TMU Problem Solving 2
A store sells apples for $0.75 each and oranges for $1.25 each.
If Maria spends exactly $10.00 buying a total of 10 pieces of fruit, how many apples did she buy?