Numerical Reasoning: Bases, Units and Checks
Work through percentages, weighted means, rate conversions and table shares using explicit denominators, unit labels and independent plausibility checks.
Read this full public learning guide before or after practice. It is identical for everyone. Your private on-page record separately shows correct, wrong and unanswered counts out of six; no percentile, employer cutoff or ability level is inferred.
Define the requested quantity
- Before calculating, write a short label for what the question requests: percentage increase, mean per batch, final count, converted total, share of a combined total or distance. Similar-looking numbers can answer different questions. A percentage increase uses the earlier amount as its base; a share uses the specified whole. Copying the right values into the wrong relationship is still a reasoning error, even if every arithmetic step is accurate.
- All data in this part are fictional practice inputs. The alpha-to-beta conversion is a stated exercise rule, not a current exchange rate or financial recommendation. The conveyor uses ideal constant speed, not evidence that real equipment works without stops. Keep the model assumptions attached to the calculation. These six questions practise interpreting supplied information; they do not certify job performance, numeracy level or operational safety.
Percent change needs an original base
- Use (new minus old) divided by old for a percentage increase, then multiply by one hundred. A fresh example is a count rising from 120 to 150: the increase is 30, which is one quarter of 120, giving twenty-five percent. Dividing by 150 would instead describe the increase as a share of the final amount. State the denominator in words before reaching for a calculator.
- Successive percentage changes use successive bases. If a fictional quantity of 100 falls by twenty percent and then rises by twenty percent, it becomes 80 and then 96. The equal percentages do not cancel because they multiply different amounts. A compact factor calculation, 100 × 0.8 × 1.2, preserves that structure and helps you spot the tempting but incorrect return to exactly 100.
Count observations before averaging
- A mean per batch weights each actual batch equally. If two batches hold 12 units and one holds 30, the total is 54 across three batches, giving 18. Averaging the two displayed sizes, 12 and 30, gives 21 but ignores their frequencies. Make a tiny frequency table or expand the observations when you are uncertain which units are being averaged. The denominator must count the requested observations.
- Check that an ordinary positive-weight mean lies between the smallest and largest inputs. This range check will not catch every error, but it can reject an impossible result quickly. Also distinguish a mean of individual rates from a combined rate: total output divided by total time is not always the unweighted average of separately reported rates. Use the relationship the prompt defines rather than assuming all displayed values carry equal weight.
Carry units through conversions
- A conversion factor should cancel the old unit and leave the requested one. If one fictional token equals two credits, five tokens become ten credits, not two and a half. A fixed credit fee is added in credits after conversion unless the prompt states another sequence. Writing token × credit per token exposes the direction and prevents multiplying an already converted fee a second time.
- For rate problems, align time units before multiplication. A fresh example is 0.4 metres per second for one and a half minutes: ninety seconds times 0.4 gives thirty-six metres. Multiplying 0.4 by 1.5 would mix seconds and minutes. Keep enough precision during the working, then round only if the question explicitly requests a rounded value or the answer format makes that requirement clear.
Read totals and table shares
- When asked what fraction of a two-period total belongs to one period, add both periods for the denominator. With 40 tasks in one month and 60 in another, the second month supplies sixty out of one hundred, or sixty percent. Dividing sixty by forty answers a comparison between months. Read the nouns attached to “of” and “relative to”; those words often identify the whole you need.
- Check whether totals overlap, whether categories are exclusive and whether every row uses the same unit. This bank states simple non-overlapping inputs, but the habit matters when moving to a fresh table. Do not silently add people to transactions or treat cumulative figures as separate monthly counts. When necessary information is genuinely absent, name the missing definition rather than inventing a plausible number to finish an arithmetic routine.
Use time without hiding assumptions
- This site gives six numerical questions five minutes in timed mode, the longest cap in this mixed bank. It is an editorial practice choice, not a provider rule or measured target pace. Paper and a calculator are allowed here. Use them to externalise a relationship and check arithmetic, rather than letting calculator digits replace the decision about which numbers, units and denominator belong in the formula.
- You can return within the active part, explicitly leave an item unanswered, or finish early. At expiry, untouched items remain unanswered rather than being recorded as selected wrong answers. Untimed study lets you inspect each relationship before practising with a cap. Your actual employer assessment may permit different equipment and navigation, so check its instructions instead of transferring this site’s rules into that setting.
Turn a wrong answer into a fresh example
- After all parts close, inspect the worked explanation and classify the first error: base, frequency, conversion direction, time unit, sequence of changes or arithmetic. Then create one different-number example with the same relationship and solve it without looking at the original option letters. Check the result with a rough bound, a reverse calculation or a second representation. That review produces a specific practice target rather than a broad label.
- The raw record is out of six and contains no calibrated numerical score, percentile or pass band. Repeating a fixed bank can improve recognition; it cannot by itself demonstrate transfer to unfamiliar tasks. This public guide remains the same for every reader and carries no personal count in its URL. Use it to plan one bounded next exercise, while following the exact provider invitation for an actual assessment.