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Mathematics Flashcards

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

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  1. A clock loses 4 minutes every 2 hours. It shows the correct time at 6:00 AM. What time will the clock display when the actual time is 9:00 PM that same day?

    Answer: 8:30 PM

    From 6:00 AM to 9:00 PM is 15 hours. The clock loses 4 minutes every 2 hours, which is 2 minutes per hour. Over 15 hours it loses 15 × 2 = 30 minutes. The clock therefore displays 9:00 PM − 30 minutes = 8:30 PM.

  2. If log₂(x) + log₂(x − 6) = 4, what is the value of x?

    Answer: 8

    Apply the logarithm product rule: log₂(x(x−6)) = 4, so x(x−6) = 2⁴ = 16. This gives x² − 6x − 16 = 0, which factors as (x−8)(x+2) = 0, yielding x = 8 or x = −2. Since logarithms require positive arguments and x − 6 must also be positive (x > 6), only x = 8 is valid. Check: log₂(8) + log₂(2) = 3 + 1 = 4 ✓

  3. A tank is 3/4 full of water. After removing 15 liters, the tank is exactly 1/2 full. What is the total capacity of the tank?

    Answer: 60 L

    Let the capacity be C liters. The volume removed equals the difference between the two fill levels: (3/4)C − (1/2)C = 15. Simplifying: (3/4 − 2/4)C = (1/4)C = 15, so C = 60 liters. Verify: 3/4 × 60 = 45 L; 45 − 15 = 30 L = 1/2 × 60 ✓

  4. What is the units digit of 7⁹⁷?

    Answer: 7

    The units digits of successive powers of 7 follow a repeating cycle of length 4: 7¹→7, 7²→9, 7³→3, 7⁴→1, 7⁵→7, … To find the position in the cycle, compute 97 mod 4 = 1 (since 96 = 4 × 24). A remainder of 1 corresponds to the first position in the cycle, which has units digit 7.

  5. Pipe A fills a tank in 12 hours, Pipe B fills it in 18 hours, and Pipe C drains it in 9 hours. If all three operate simultaneously on an empty tank, how many hours will it take to fill the tank completely?

    Answer: 36 hours

    Combined hourly rate: A adds 1/12, B adds 1/18, C removes 1/9. Using a common denominator of 36: 3/36 + 2/36 − 4/36 = 1/36 per hour (net fill). Since the net rate is positive, the tank does fill, and it takes 36 hours to reach capacity.

  6. A sequence is defined by aₙ = aₙ₋₁ + aₙ₋₂ + 2 for n ≥ 3, with a₁ = 1 and a₂ = 2. What is the value of a₆?

    Answer: 27

    Applying the recurrence step by step: a₃ = 2 + 1 + 2 = 5; a₄ = 5 + 2 + 2 = 9; a₅ = 9 + 5 + 2 = 16; a₆ = 16 + 9 + 2 = 27. Each term is the sum of the two preceding terms plus the constant 2.