Arithmetic reasoning without a calculator
These items reward structure over calculation. Each family has a shortcut that turns a messy sum into one step.
Reverse percentages
A total of 1,18,000 including 18 per cent tax is 1.18 times the base, so divide rather than subtract 18 per cent. Subtracting is the intended error.
Successive changes
A 40 per cent markup followed by a 25 per cent discount multiplies cost by 1.40 then 0.75, giving 1.05 — a 5 per cent profit. Percentages compose by multiplication, never addition.
Combined rates
Two taps filling in 12 and 18 minutes add rates, not times: one twelfth plus one eighteenth is five thirty-sixths, so 36/5 minutes, 7 minutes 12 seconds.
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Questions people ask
How much mental arithmetic is needed?
Very little if you set the structure up correctly; the numbers stay deliberately small.
Is rough estimation enough?
Often yes — estimating first eliminates two or three options immediately.