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Mathematical & Numerical Reasoning Flashcards

6 cards from real Ramsay Test 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 pump fills a tank in 6 hours. A second pump drains the same tank in 9 hours. Both pumps run simultaneously, and the tank starts at 1/3 capacity. How long will it take to completely fill the tank?

    Answer: 12 hours

    Net fill rate = 1/6 − 1/9 = 3/18 − 2/18 = 1/18 of the tank per hour. Since the tank is already 1/3 full, 2/3 remains. Time = (2/3) ÷ (1/18) = (2/3) × 18 = 12 hours.

  2. A drive gear with 48 teeth meshes with an intermediate gear of 36 teeth, which in turn meshes with an output gear of 24 teeth. If the drive gear spins at 75 RPM, what is the speed of the output gear?

    Answer: 150 RPM

    Apply the gear ratio at each mesh: Gear 2 = 75 × (48/36) = 100 RPM. Gear 3 = 100 × (36/24) = 150 RPM. Each smaller driven gear spins faster than the gear driving it, and the ratios compound multiplicatively.

  3. A replacement part costs $240 after two successive price increases: first 25%, then 20%. What was the original price before either increase?

    Answer: $160

    Successive multipliers compound: original price P × 1.25 × 1.20 = P × 1.50 = $240, so P = $240 ÷ 1.50 = $160. The combined effect is a 50% total increase, not 45% — percentages do not simply add.

  4. A rectangular steel plate is 2.5 m long, 1.2 m wide, and 8 mm thick. Steel density is 7,850 kg/m³. What is the mass of the plate to the nearest kilogram?

    Answer: 188 kg

    Convert thickness: 8 mm = 0.008 m. Volume = 2.5 × 1.2 × 0.008 = 0.024 m³. Mass = 0.024 × 7,850 = 188.4 ≈ 188 kg. A common mistake is omitting the unit conversion for thickness, which inflates the answer by a factor of 125.

  5. Technicians X, Y, and Z together complete a repair job in 3 hours. X and Y together take 6 hours; X and Z together take 4 hours. How long would technician X take working alone?

    Answer: 12 hours

    Using rates (jobs/hour): x+y+z = 1/3, x+y = 1/6, so z = 1/3 − 1/6 = 1/6. Then x+z = 1/4, so x = 1/4 − 1/6 = 3/12 − 2/12 = 1/12. X alone takes 12 hours. A common error is averaging the given times instead of working with rates.

  6. A wire 3.6 m long made of a given material has a resistance of 4.5 Ω. A second wire of the same material is 2.4 m long but has twice the cross-sectional area. What is the resistance of the second wire?

    Answer: 1.5 Ω

    R = ρL/A. The ratio R₂/R₁ = (L₂/L₁) × (A₁/A₂) = (2.4/3.6) × (1/2) = (2/3) × (1/2) = 1/3. Therefore R₂ = 4.5 × (1/3) = 1.5 Ω. Doubling the area halves resistance; the shorter length reduces it further.