Mechanical Reasoning Tests | Shop Arithmetic

Some of the questions you come across may require knowledge of basic mathematics, fractions, decimals, ratios, percentages, and averages. These basic mathematical skills are an important aspect of mechanical ability and making basic calculations on the basis of the information provided and your knowledge of mechanical principles is part of these tests.


You will need to know the formulae for calculating the areas and volumes of simple shapes, as well as familiarity with imperial units including: inches, feet and yards. For example, you need to know that there are nine square feet in a square yard, something which surprises many people brought up using only metric units!

Some useful formulas include: Areas,


the volume of rectangular solids and cylinders,


and some simple geometry like Pythagoras Theorem.


Example Shop Arithmetic Questions


The sketch above shows a component which is stamped out of sheet steel. The square in the center is discarded. These components are stamped out of a continuous steel coil with a width of 70 cms. The stamping process requires a gap of 25mm between each component. The steel coil is supplied in lengths of 25 meters costing $200.

1) What is the approximate area of the remaining shape in square centimetres?

  • A) 1938

  • B) 1855

  • C) 1926

  • D) 1998

  • E) 1760

2) What is the approximate percentage of steel wasted including the center square?


  • A) 56%

  • B) 50%

  • C) 62%

  • D) 48%

  • E) 52%

3) Assuming minimal wastage, how many components can be produced from each 25 meter coil?

  • A) 38

  • B) 40

  • C) 36

  • D) 42

  • E) 37

4) What is the approximate cost of a component if the scrap is sold at 50% of cost?

  • A) $3.60

  • B) $3.15

  • C) $3.55

  • D) $5.00

  • E) $4.85


The sketch shows a component made from 5cm square bar and 5cm diameter rod. The density of steel is 8g per cubic centimetre. For shipping purposes the components are packed into individual boxes before being packed into shipping crates measuring approximately 0.25m x 0.3m x 0.4m. Shipping crates are packed on pallets to a maximum weight of 800 Kg.

5) What is the approximate total volume of the component in cubic centimetres?

  • A) 655

  • B) 788

  • C) 967

  • D) 422

  • E) 892

6) What is the approximate weight of the component?

  • A) 72.4 Kg

  • B) 7.14 Kg

  • C) 7.34 Kg

  • D) 14.4 Kg

  • E) 5.14 Kg

7) How many boxed components can be fitted into a shipping crate?

  • A) 48

  • B) 24

  • C) 22

  • D) 20

  • E) 18

8) How many shipping crates can be fitted onto a palette?

  • A) 5

  • B) 4

  • C) 7

  • D) 6

  • E) 12

Answers to Questions

  1. C

  2. A

  3. B

  4. C

  5. E

  6. B

  7. D

  8. A

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