How to Solve Mechanical Reasoning Questions: A Four-Step Method

People who do well on mechanical reasoning tests are not guessing faster. They run the same short routine on every question, and it works for levers, gears, pulleys, springs and fluids alike.

Why a Routine Helps

Research reviewed by Hegarty (2004) found that people often reason about machines by mental simulation. Those simulations are built piecemeal, not as one picture seen in the mind's eye, and they can be combined with rule-based reasoning and with breaking a task into parts. That combination is what the routine below makes deliberate.

People differ in how well they do this. Hegarty and Sims (1994) tested how spatial visualization ability affects performance on a task of judging how a mechanical system moves, and Hegarty and Steinhoff (1997) examined individual differences in how people use a diagram as external memory when reasoning about a machine. On a test, your scrap paper is the nearest equivalent to that external memory. A fixed routine, written down, takes load off your head and leaves attention for the physics.

The Four Steps

1. Name the trade. Which machine is it, and what is being swapped? Nearly every machine trades force for distance or for speed. Saying which one points you at the rule.
2. Write the rule. Put the equation on paper before any numbers: effort x effort arm = load x load arm; speed out = speed in x teeth in / teeth out; effort = load / sections; pressure = force / area; force = k x extension.
3. Substitute with units. One line per step. Units catch many errors, such as mixing cm² and m², before they reach the answer.
4. Sense-check. Ask whether the answer is the right size and the right direction, and whether work in equals work out.

A Worked Example

A lever lifts a 900 N load that sits 0.2 m from the pivot. The effort is applied 1.5 m from the pivot on the other side. What effort balances the load?

1. Name the trade: a lever trades force for distance.
2. Rule: effort x effort arm = load x load arm.
3. Substitute: E x 1.5 = 900 x 0.2 = 180, so E = 120 N.
4. Check: the effort arm (1.5 m) is longer than the load arm (0.2 m), so the effort should be smaller than the load. 120 N is smaller than 900 N. The size is right.

The check also explains the tempting wrong answer. Flip the ratio and you get 900 x 1.5 / 0.2 = 6,750 N, a force seven times bigger than the load from a lever that is supposed to help. A number like that should fail step four immediately.

A Second Example: Hydraulics

A garage hydraulic lift has an input piston of 0.01 m² and an output piston of 0.2 m². It must support a car weighing 12,000 N. What force on the input piston holds the car up?

1. Name the trade: hydraulics trades force for distance, using the ratio of the two areas.
2. Rule: pressure is the same on both pistons, so F1 / A1 = F2 / A2.
3. Substitute: F1 = 12,000 x 0.01 / 0.2 = 600 N.
4. Check: the input piston is the smaller one, so its force should be smaller than the car's weight. 600 N is. The wrong option built from the flipped ratio is 12,000 x 0.2 / 0.01 = 240,000 N, which is far too large for a small piston to need.

When the Question Shows a Picture

Many employer tests present a drawing of a machine rather than a description in words. The routine is unchanged, with one extra first step: turn the picture into the words you would have been given. Mark the pivot of a lever, label the driver and driven gears, number the rope sections that pull on the moving block, and note which way each part turns.

The JobCannon test describes its setups in words, so use the descriptions to practise the four steps and add drawing practice from other sources before an assessment that shows pictures.

Use the Options, Too

Wrong options are rarely random. They are usually what you get after one common slip: a flipped ratio, a forgotten factor, a mixed-up unit. Computing the answer and then finding it among the options is the safe route. Eliminating the options that fail the size-and-direction check is the fast route when time is short.

Do not choose by position, or by which option looks longest or most detailed. Neither has any connection with the physics.

Make It a Habit

The routine only pays off if it is automatic, so use it on every practice question, including the easy ones. The JobCannon mechanical reasoning test gives an explanation after each question, and the mechanical reasoning practice page has solved examples. Speed comes later: see how much time you get per question, and learn what the usual slips look like in common mistakes on mechanical reasoning tests.