Ramsay Test Mathematical & Numerical Reasoning 5

Question 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?

Accepted Answer

12 hours

Answer

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.

Question 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?

Accepted Answer

150 RPM

Answer

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.

Question 3

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

Accepted Answer

$160

Answer

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.

Question 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?

Accepted Answer

188 kg

Answer

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.

Question 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?

Accepted Answer

12 hours

Answer

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.

Ramsay Test Practice Test

Ramsay Test Practice Test

Ramsay Test Mathematical & Numerical Reasoning 5