Practice Test Geeks(BCA) Bergen County Academies Practice Test
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Problem Solving Flashcards

7 cards from real BCA practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 7 Problem Solving flashcards as text

  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?

    Answer: 64 gallons

    (3/4 − 1/3) × C = 24; (5/12) × C = 24; C = 64 gallons.

  2. If f(x) = 2x² − 3x + 1, what is f(−2)?

    Answer: 15

    f(−2) = 2(4) − 3(−2) + 1 = 8 + 6 + 1 = 15.

  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?

    Answer: 12 feet

    By the Pythagorean theorem: h = √(13² − 5²) = √(169 − 25) = √144 = 12 feet.

  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?

    Answer: $1,000

    Total parts = 10; largest share = (5/10) × $2,000 = $1,000.

  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?

    Answer: 2 hours

    Combined speed = 150 mph; time = 300 ÷ 150 = 2 hours.

  6. Which strategy is most effective when a problem has too many variables to solve directly?

    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.

  7. A 6-sided die is rolled twice. What is the probability that both rolls show a prime number?

    Answer: 1/4

    Primes on a die: {2, 3, 5} = 3 faces; P = (3/6)² = (1/2)² = 1/4.