BCA Problem Solving 3 — Questions and Answers
Question 1: A water tank is 1/3 full. After adding 24 gallons, it is 3/4 full. What is the total capacity of the tank?
- 48 gallons
- 56 gallons
- 64 gallons (Correct answer)
- 72 gallons
Correct answer: 64 gallons
(3/4 − 1/3) × C = 24; (5/12) × C = 24; C = 64 gallons.
Question 2: If f(x) = 2x² − 3x + 1, what is f(−2)?
- 11
- 15 (Correct answer)
- 3
- 7
Correct answer: 15
f(−2) = 2(4) − 3(−2) + 1 = 8 + 6 + 1 = 15.
Question 3: A ladder 13 feet long leans against a wall. The base is 5 feet from the wall. How high up the wall does the ladder reach?
- 10 feet
- 11 feet
- 12 feet (Correct answer)
- 8 feet
Correct answer: 12 feet
By the Pythagorean theorem: h = √(13² − 5²) = √(169 − 25) = √144 = 12 feet.
Question 4: A prize is split among three people in the ratio 2:3:5. If the total prize is $2,000, how much does the person with the largest share receive?
- $400
- $600
- $800
- $1,000 (Correct answer)
Correct answer: $1,000
Total parts = 10; largest share = (5/10) × $2,000 = $1,000.
Question 5: Two trains start from cities 300 miles apart and travel toward each other. Train A goes 60 mph and Train B goes 90 mph. In how many hours do they meet?
- 1.5 hours
- 2 hours (Correct answer)
- 2.5 hours
- 3 hours
Correct answer: 2 hours
Combined speed = 150 mph; time = 300 ÷ 150 = 2 hours.
Question 6: Which strategy is most effective when a problem has too many variables to solve directly?
- Guess randomly and check
- Reduce to a simpler related problem (Correct answer)
- Ignore unnecessary constraints
- Solve only part of the problem
Correct answer: Reduce to a simpler related problem
Reducing to a simpler related problem is a core problem-solving heuristic that builds insight into complex cases.
Question 7: A 6-sided die is rolled twice. What is the probability that both rolls show a prime number?
- 1/4 (Correct answer)
- 1/2
- 1/3
- 2/9
Correct answer: 1/4
Primes on a die: {2, 3, 5} = 3 faces; P = (3/6)² = (1/2)² = 1/4.
BCA Problem Solving 3
A water tank is 1/3 full.
After adding 24 gallons, it is 3/4 full.
What is the total capacity of the tank?