Wrong answers have names
The most common numerical reasoning mistakes — named, explained, fixed.
Using the wrong base in percentage change
Percentage change is always measured against the ORIGINAL value: (new − old) ÷ old.
The fixReading the adjacent cell
The most common table mistake isn't arithmetic at all — it's pulling the number from the row above, the column beside, or a similarly named header, then computing perfectly with the wrong data.
The fixDividing by the wrong total
"What share is X?" means X ÷ (the relevant total).
The fixThe decimal slip
An answer that's exactly 10× or 100× off isn't a maths error — it's a decimal slip: a percentage not converted (×5 instead of ×0.
The fixAveraging averages without weights
Combining two group means by simple averaging is only valid when the groups are the same size.
The fixRearranging speed–distance–time wrongly
Speed = distance ÷ time, and the other two follow by rearrangement: distance = speed × time, time = distance ÷ speed.
The fixInverting the rate
Converting with a rate goes one way; the return trip divides.
The fixStopping one step early
A multi-step question's intermediate result is almost always among the answer options.
The fixConcluding what the data doesn't say
In True/False/Cannot-say questions, 'Cannot say' is correct whenever the statement needs information the exhibit doesn't contain — however plausible the statement sounds.
The fixAnswering the complement
Computing the probability (or percentage) of the event when the question asked for its opposite — or vice versa.
The fixConfusing absolute and relative change
"Which grew most?" has two correct answers depending on the question: the biggest absolute change (in units) or the biggest relative change (in %).
The fixDoubling instead of compounding
Two years of 10% growth is ×1.
The fix