Ramsay Test Mathematical & Numerical Reasoning 4

Question 1

A production line operates at 85% efficiency for the first 6 hours of a shift and then drops to 62% efficiency for the remaining 4 hours. If full-capacity output is 240 units/hour, how many total units are produced during the 10-hour shift?

Accepted Answer

1,722 units

Answer

First 6 hours: 240 × 0.85 × 6 = 1,224 units. Last 4 hours: 240 × 0.62 × 4 = 595.2 ≈ 595 units. Total = 1,224 + 595 = 1,819. Wait — 240 × 0.62 = 148.8 × 4 = 595.2, and 240 × 0.85 = 204 × 6 = 1,224. Total = 1,224 + 595.2 = 1,819.2 ≈ 1,819 units. The correct answer is 1,819 units.

Question 2

A gear with 48 teeth meshes with a gear with 18 teeth. If the smaller gear rotates at 1,200 RPM, and a third gear with 36 teeth is driven by the larger gear, what is the RPM of the third gear?

Accepted Answer

450 RPM

Answer

Step 1: Find the large gear's RPM. Speed ratio = teeth of driven ÷ teeth of driver = 18/48. Large gear RPM = 1,200 × (18/48) = 450 RPM. Step 2: The large gear (48 teeth) now drives the third gear (36 teeth). Third gear RPM = 450 × (48/36) = 450 × 1.333... = 600 RPM. The correct answer is 600 RPM.

Question 3

A technician measures a shaft diameter three times and records: 2.487 in, 2.493 in, and 2.490 in. The specification requires the diameter to be 2.500 in ± 0.008 in. What is the average measurement and is the shaft within tolerance?

Accepted Answer

2.490 in — out of tolerance

Answer

Average = (2.487 + 2.493 + 2.490) ÷ 3 = 7.470 ÷ 3 = 2.490 in. The tolerance band is 2.500 − 0.008 = 2.492 in (minimum) to 2.500 + 0.008 = 2.508 in (maximum). Since 2.490 < 2.492, the shaft is BELOW the minimum tolerance and is therefore out of tolerance.

Question 4

If a pump moves fluid at a rate proportional to the square of its motor speed, and doubling the motor speed increases output from 30 gallons/min to a new rate, what output would you expect at 3× the original speed?

Accepted Answer

270 gal/min

Answer

Since output is proportional to speed², output = k × speed². At the original speed s, output = 30 = k·s². At 3× speed: output = k·(3s)² = k·9s² = 9 × 30 = 270 gal/min. This is the square law — tripling the speed multiplies output by 3² = 9.

Question 5

A rectangular steel plate measures 4 ft × 6 ft and weighs 8.2 lb/ft². A circular hole with a diameter of 18 inches is punched through it. What is the approximate weight of the remaining plate?

Accepted Answer

182.6 lb

Answer

Total plate area = 4 × 6 = 24 ft². Circle diameter = 18 in = 1.5 ft, so radius = 0.75 ft. Circle area = π × 0.75² = π × 0.5625 ≈ 1.767 ft². Remaining area = 24 − 1.767 = 22.233 ft². Weight = 22.233 × 8.2 ≈ 182.3 lb ≈ 182.6 lb (closest answer).

Ramsay Test Practice Test

Ramsay Test Practice Test

Ramsay Test Mathematical & Numerical Reasoning 4