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- International Student Admissions Mathematical Problem-Solving Flashcards

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

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  1. Bacteria doubles every 4 hours, starting with 500. How many after 24 hours?

    Answer: 32,000

    Doublings = 24/4 = 6. Population = 500 x 2^6 = 500 x 64 = 32,000.

  2. A 10m ladder: base 6m from wall. Base slides 2m further out. How much does the top slide down?

    Answer: 2 meters

    Original height: sqrt(100-36) = 8m. New height: sqrt(100-64) = 6m. Difference: 2m.

  3. A cone: radius 5cm, height 12cm. Filled to half height. What fraction of total volume is filled?

    Answer: 1/8

    At half height, radius is halved. Volume scales as cube of linear dimension: (1/2)^3 = 1/8.

  4. A car depreciates 15% per year from $24,000. Value after 3 years?

    Answer: $14,731

    24000 x 0.85^3 = 24000 x 0.614125 = $14,739.

  5. Two trains 480km apart travel toward each other at 70 and 90 km/h. When and where do they meet?

    Answer: 3 hours; 210 km from A

    Combined speed = 160 km/h. Time = 480/160 = 3 hours. Distance from A = 70 x 3 = 210 km.

  6. Circular track: 400m circumference. Runner A: 5 m/s. Runner B: 3 m/s. Same direction. When does A first lap B?

    Answer: 200 seconds

    Relative speed = 2 m/s. A must gain 400m. Time = 400/2 = 200 seconds.