Irish Numerical Reasoning common mistakes
Irish Numerical Reasoning · Understand the traps and how to avoid them.
Assuming the gap between consecutive terms is constant and adding that same difference to the last term, when the differences themselves form a pattern (e.g. +2, +4, +6, +8).
The first two or three gaps look uniform enough to trigger a 'constant difference' habit, so the candidate stops checking once a plausible rule appears.
What to do instead
Always compute the full table of first differences for every adjacent pair before committing to a rule. If they are not all equal, compute second differences. Only accept a rule that explains every term you have been given.
Treating a series as arithmetic when the ratio between terms is constant, or vice versa, because the first two terms are ambiguous (e.g. 3, 9, ...).
With only two terms, both a difference rule and a ratio rule fit, and candidates pick whichever they thought of first rather than testing both against later terms.
What to do instead
For any series, explicitly test both 'add d' and 'multiply by r' against the third and fourth terms. Use the term that only one rule predicts as the discriminator.
Reading the question as asking for the final value when it asks for the change (or the percentage change), and selecting the matching distractor.
The computation produces a number that appears among the options, so the candidate feels finished and does not re-read the final sentence of the stem.
What to do instead
Before computing, write down in one line what quantity the answer must be (new value, change, or % change) and its units. After computing, check the answer against that written target.
Applying successive percentage changes by adding or subtracting them (treating +20% then -20% as no change).
Percentages feel additive because they are written with a plus or minus sign, and the base of the second change is forgotten.
What to do instead
Convert each percentage to a multiplier (1.20, 0.80) and multiply the multipliers. Verify with a concrete base of 100 whenever the numbers allow.
Splitting a total in a given ratio by dividing by the number of parts in the ratio but then assigning the whole quotient to one share, or dividing by the number of people rather than the number of parts.
The candidate conflates 'number of shares' with 'number of recipients', which are often different numbers in the stem.
What to do instead
Write the ratio as parts, sum the parts, divide the total by the sum to get one part, then multiply by the specific part required. Check that the shares add back to the original total.
Using the wrong base when computing a percentage of a total taken from a table, e.g. dividing a row value by the column total when the question asks for a share of the row.
Tables present row and column totals side by side and the stem's phrasing ('of those who...') is easy to skim past.
What to do instead
Underline the phrase after 'of' or 'out of' in the stem; that phrase names the denominator. Circle the corresponding total in the table before dividing.
Averaging two speeds over equal distances (e.g. 60 km/h and 40 km/h taken as 50 km/h) instead of using total distance over total time.
The arithmetic mean of two speeds is intuitive and lands on a round number that is usually offered as a distractor.
What to do instead
For any journey described in legs, compute total distance and total time separately and divide once at the end. Only average speeds directly when the times (not distances) are equal.
Adding work rates as if they were times, e.g. two workers taking 6 and 12 hours being combined as 6 + 12 rather than 1/6 + 1/12 per hour.
The numbers in the stem are times, and the candidate performs the operation on the numbers as written instead of converting to a rate first.
What to do instead
Convert every worker to a fractional rate per unit time, sum the rates, then invert to get the combined time. Sanity-check that the combined time is less than the fastest individual time.
Rounding intermediate results to convenient numbers and then reporting the rounded figure as exact, or rounding in the wrong direction when the options are close together.
Estimation is encouraged for speed, and candidates carry the estimated value straight through to answer selection.
What to do instead
Estimate first to bracket the answer and eliminate options, then compute exactly with the original numbers for the final choice. Keep at least one more digit than the options show at each intermediate step.
Misaligning units across a rate problem, e.g. mixing minutes and hours, or centimetres and metres, so the numeric answer is out by a factor of 60 or 100.
Stems often give one quantity in minutes and the answer options in hours, and the conversion step is invisible once the arithmetic starts.
What to do instead
At the start, convert every given quantity to a single consistent unit set and annotate the units next to each number. Before selecting, confirm the answer's units match those requested in the stem.