Ramsay Test Mathematical & Numerical Reasoning 6

Question 1

A machine's output rate increases by 15% in the first month and then decreases by 12% in the second month. What is the net percentage change compared to the original rate?

Accepted Answer

1.2% increase

Answer

You cannot simply subtract the percentages. The correct method is to multiply the factors: 1.15 × 0.88 = 1.012, which represents a 1.2% net increase. Subtracting 15% − 12% = 3% is the common mistake — it ignores that the 12% decrease applies to the already-increased value, not the original.

Question 2

A gear train has three meshing gears in series. Gear A has 24 teeth and spins at 180 RPM. It drives Gear B, which has 36 teeth. Gear B drives Gear C, which has 18 teeth. What is the rotational speed of Gear C?

Accepted Answer

240 RPM

Answer

Speed is inversely proportional to tooth count. Gear B speed = 180 × (24/36) = 120 RPM. Gear C speed = 120 × (36/18) = 240 RPM. Each gear ratio is applied in sequence. A common error is to apply a single overall ratio of 24/18 directly to 180 RPM, which ignores how intermediate gears transmit motion.

Question 3

A technician must blend 80 lbs of an alloy containing exactly 35% copper. She has stock alloy A at 20% copper and stock alloy B at 50% copper. How many pounds of alloy B (50% copper) should she use?

Accepted Answer

40 lbs

Answer

Set x = lbs of the 50% alloy; (80 − x) = lbs of the 20% alloy. The copper equation is: 0.50x + 0.20(80 − x) = 0.35 × 80 → 0.50x + 16 − 0.20x = 28 → 0.30x = 12 → x = 40 lbs. Note that the answer is exactly the midpoint because 35% is midway between 20% and 50%.

Question 4

A pump transfers fluid at 45 gallons per minute. Approximately how many cubic feet of fluid does it move in one hour? (Use: 1 gallon ≈ 0.1337 cubic feet)

Accepted Answer

361.0 cu ft

Answer

First convert the rate to gallons per hour: 45 gal/min × 60 min/hr = 2,700 gal/hr. Then convert to cubic feet: 2,700 × 0.1337 ≈ 361.0 cu ft. A frequent error is forgetting to convert minutes to hours before multiplying by the conversion factor, yielding the distractor 36.1 cu ft.

Question 5

A production line runs at 120 units/hour. A mechanical fault drops efficiency to 75% for the first 3 hours; it then recovers to 90% for the following 5 hours. What is the total output over the full 8-hour period?

Accepted Answer

810 units

Answer

Calculate each segment separately. First 3 hours: 120 × 0.75 × 3 = 270 units. Next 5 hours: 120 × 0.90 × 5 = 540 units. Total: 270 + 540 = 810 units. Using a single blended efficiency for the whole period (a common shortcut) gives an incorrect result because the time-weighted average is not 82.5%.

Ramsay Test Practice Test

Ramsay Test Practice Test

Ramsay Test Mathematical & Numerical Reasoning 6