GAMSAT Section III mental maths: the arithmetic worth drilling

Two weeks out, the highest-yield hour left in Section III is not more content. It is arithmetic - because arithmetic is the one part of the section that is pure tax. Nobody earns a mark for computing well; you simply lose marks when computing slowly. With no calculator, 75 questions and 150 minutes, every clumsy long division is paid for out of the thinking budget of a later question.

Arithmetic is not the skill being tested - it is the toll on it

Section III gives you the science and asks whether you can reason with it. The numbers are there to make you draw a conclusion, and the conclusion almost never depends on the third decimal place. That is the whole opening: most candidates compute far more precisely than the question requires, then run short on the questions that actually needed the time.

Estimate first, and let the options do the work

The options are part of the data. Before computing anything, look at how far apart they are - if they differ by an order of magnitude, one significant figure decides it, and you are done in ten seconds. Only when two candidates survive the estimate do you sharpen, and then only far enough to separate those two.

Worked: 4.2 x 10⁻³ multiplied by 3.1 x 10⁵. Round to 4 x 3 = 12, and 10⁻³ x 10⁵ = 10², so roughly 1.2 x 10³. The exact value is 1302 - the estimate is within about 8%, which separates any sensible option set. If two options sit at 1.2 x 10³ and 1.3 x 10³, then you refine.

Powers of ten, moved in your head

Almost all Section III arithmetic is small numbers plus an exponent. Keep them apart: multiply the mantissas, add the exponents, and normalise at the end. The errors that cost marks are nearly always exponent errors, not digit errors - and an exponent error is usually visible, because the answer comes out absurd for the quantity being measured.

The number facts worth knowing cold

These are not clever - they are just the ones that recur, and recall beats computation every time. If you have to derive that 3/8 is 37.5% under exam pressure, you have spent fifteen seconds on something that should cost none.

Ratio, proportion and "what happens if"

A large share of Section III questions are proportional reasoning in disguise: not "compute the value" but "which way, and by how much, does it move". Learn to answer those without computing the original value at all. If a rate doubles every 20 minutes, an hour is three doublings, so ×8. Triple the distance from a point source and intensity falls to a ninth. Scale a cell's radius by 2 and surface area goes ×4 while volume goes ×8 - which is the whole surface-area-to-volume argument in one line.

Percentage change has an asymmetry worth rehearsing too: 250 up to 300 is +20%, but 300 back down to 250 is -16.7%. Questions that offer both numbers are usually testing exactly that.

Logs, pH and orders of magnitude

You will not be asked to evaluate a logarithm precisely, but you will be asked to move between a concentration and a pH, or to say how many times bigger one quantity is than another. Two facts carry nearly all of it: log 2 ≈ 0.30 and log 3 ≈ 0.48. From those, pH of a 2 x 10⁻⁵ M strong acid solution is 5 − 0.30 = 4.7, and you never touch a calculator.

Units: convert once, at the start

Mixed units cause more wrong answers in Section III than any arithmetic slip, because the number that comes out looks perfectly reasonable. Convert everything into one system before you compute, write the units next to the working, and let the units check the answer: if the algebra produces grams where the question asks for grams per litre, the error is upstream of the arithmetic. Some conversions are worth having by heart - 1 µg/mL is 1 mg/L, 1 mmol/L is 1 mM, 36 km/h is 10 m/s.

How to drill it: ten minutes, mixed and timed

Blocked practice ("twenty exponent questions") builds false confidence, because you already know which move to make. Mixed practice under a clock is what transfers: ten minutes a day of scrambled estimation, exponents, fractions, proportion and unit conversion, always out loud or on paper, never with a calculator within reach. Then take it into full sets - timed Section III practice records your per-question times, and those times are where you see the arithmetic tax being paid. A free account covers 5 questions with the worked explanation for each; the rest of the bank is Pro.

Two weeks of that is not a content gain. It is a time gain in a double-weighted section - which is the same thing, only cheaper.

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