Lesson 32 of 42 · Numerical reasoning
Separating relevant from superfluous information
Start from the question, write the formula it needs, and take only those inputs from the data, so extra figures cannot pull you off course.
About 20 minutes
In this lesson
- Write the formula a data question needs before looking for numbers.
- Recognise the usual kinds of superfluous information and ignore them.
- Tell when an essential input is missing, so that the answer cannot be determined.
The idea
More data than you need
Data questions often give more information than the question needs: extra columns in a table, an extra year, figures for a group the question does not ask about, a cost when the question is about a quantity. That is not a trick in itself; real reports look like that. It becomes a trap when you start computing with the first numbers you see instead of with the numbers the question requires.
Start from the question, not the data
The reliable method runs backwards.
- Name the target. What quantity, in what unit, for which group and which period? "Revenue per kilogram" is not "revenue", and "in March" is not "in the first quarter".
- Write the formula. Revenue = quantity × price. Fuel used = distance × consumption per km. Profit margin = profit ÷ revenue. Room revenue per night = rooms × occupancy rate × price per room.
- Fill the formula. Go to the data for exactly the inputs the formula needs. Everything else is, for this question, noise.
Writing the formula first protects you from the commonest error, which is using a number because it is there.
Typical superfluous information
| Kind | Example |
|---|---|
| A column the formula does not use | Number of staff, when the question is about revenue |
| A different period | Annual figures, when the question asks about one month |
| A different group | Data for all employees, when the question is about part-time staff |
| A total that already contains the part | Total costs and fixed costs, when only variable costs are asked for |
| A figure that matches an option | A number in the data that appears among the options but answers a different question |
Information that is the same for everyone
When a quantity is the same for every item being compared (one fuel price for all vans, one tax rate for all firms), it cannot change a ranking. You need it to compute an amount in euros, but not to decide which item is cheapest. Spotting this saves time and removes a chance to slip.
When something essential is missing
The opposite also happens: the data may lack an input the formula needs. A profit margin rising from 8% to 10% does not tell you whether profit rose, because profit = margin × revenue and revenue is not given. If revenue fell from €1,000,000 to €700,000, profit fell from €80,000 to €70,000 despite the higher margin; if revenue held steady, profit rose. When an option says the answer cannot be determined, take it seriously exactly when your formula has an empty slot that no data fills.
Check consistency, not just relevance
Sometimes the same quantity can be reached two ways, for example a total given in the table and the sum of its parts. If they disagree, re-read the frame: one of them may exclude something (a category, a footnote). Use the figure that matches the question's definition.
Units are where extra data hides
Superfluous information often arrives in a different unit: grams beside kilograms, months beside years, thousands beside units, litres per 100 km beside kilometres per day. Before combining two numbers, make sure their units fit the formula, and convert once, at the start. A unit that does not cancel properly is a sign you have picked up the wrong number.
A routine
- Name the target and its unit.
- Write the formula with empty slots.
- Fill each slot from the data; cross out everything else.
- If a slot cannot be filled, consider whether the answer is undeterminable.
Worked examples
Example 1: Price per kilogram, with distractions
A shop sells coffee beans in 250 g bags for €6.50 and in 1 kg bags for €22. Last month it sold 340 of the 250 g bags, 60% of them in the first fortnight, and 85 of the 1 kg bags. The shop is open 26 days a month. How much more does a customer pay per kilogram when buying the small bags?
Name the target: price per kilogram for each bag size, then the difference. The formula is price ÷ weight in kg.
Small bags: 250 g is a quarter of a kilogram, so the price per kg is euros.
Large bags: €22 per kg already.
Difference: euros per kilogram. The numbers of bags sold, the 60% and the 26 opening days play no part.
Answer
€4 more per kilogram. Using the sales figures (for example, comparing revenue from each size) answers a different question.
Example 2: Choosing columns
| Hotel | Rooms | Occupancy rate | Average price per occupied room per night (€) | Staff |
|---|---|---|---|---|
| P | 120 | 75% | 90 | 40 |
| Q | 80 | 90% | 110 | 35 |
| R | 200 | 50% | 70 | 60 |
Which hotel earns the most room revenue per night?
Formula: room revenue per night = rooms × occupancy rate × price per occupied room. The staff column is not in the formula.
P: occupied rooms, and euros.
Q: occupied rooms, and euros.
R: occupied rooms, and euros.
Answer
Hotel P, with €8,100 a night. Q (highest price and occupancy) and R (most rooms) are tempting if you judge by a single column.
Example 3: When the data cannot answer
A firm's profit margin (profit as a percentage of revenue) rose from 8% in 2023 to 10% in 2024. Did its profit rise?
Formula: profit = margin × revenue. The margin is given for both years; revenue is not.
Try a case: revenue €1,000,000 in both years gives profit €80,000 then €100,000, a rise.
Try another: revenue €1,000,000 then €700,000 gives €80,000 then euros, a fall.
Answer
It cannot be determined from the data: the answer depends on revenue, which is missing. "Yes, because the margin rose" is the tempting wrong answer.
Common traps
Using a number because it is there
Every figure in the data feels as if it must be used. It need not be. Write the formula first; a number with no slot in the formula is noise for this question.
The number that matches an option
A figure from the table, or a quick product of two figures, appears among the options. Recognition feels like confirmation. Check that the option answers the question asked, in its unit and for its group.
Filling a missing input by assumption
When an input is missing, it is tempting to assume it stayed the same. Unless the data says so, it may not have. If an empty slot changes the answer, the answer cannot be determined.
Mixing units
Grams and kilograms, litres per 100 km and kilometres, monthly and yearly figures sit side by side. Convert everything to the units of the formula before multiplying.
Check yourself
Answer each question before you open its answer.
Question 1: Daily fuel for the medium vans
Numerical reasoning
A delivery firm's vans
| Van type | Number of vans | Fuel use (litres per 100 km) | Average daily distance per van (km) | Purchase price per van (€) |
|---|---|---|---|---|
| Small | 12 | 7 | 150 | 28,000 |
| Medium | 8 | 9 | 180 | 36,000 |
| Large | 5 | 12 | 120 | 52,000 |
Every van is driven every working day. Diesel costs €1.80 per litre.
How many litres of diesel do the medium vans use in total on an average day?
- A.16.2 litres
- B.72 litres
- C.129.6 litres
- D.233.28 litres
Show the answer
Answer: C. 129.6 litres
Working
One medium van drives 180 km at 9 litres per 100 km: litres a day. Eight vans use litres. The purchase prices, the diesel price and the other van types are not needed.
Why the other options are wrong
- A. This is one medium van's daily fuel; there are 8 of them.
- B. Multiplies the number of vans by the fuel use per 100 km, ignoring the daily distance.
- D. This is the cost of that fuel in euros (), not a quantity in litres.
What carries over
Fuel used = distance × consumption per km × number of vehicles; price and purchase cost belong to other questions.
Question 2: What is not needed?
Numerical reasoning
A delivery firm's vans
| Van type | Number of vans | Fuel use (litres per 100 km) | Average daily distance per van (km) | Purchase price per van (€) |
|---|---|---|---|---|
| Small | 12 | 7 | 150 | 28,000 |
| Medium | 8 | 9 | 180 | 36,000 |
| Large | 5 | 12 | 120 | 52,000 |
Every van is driven every working day. Diesel costs €1.80 per litre.
To decide which van type has the lowest fuel cost per kilometre, which of the given information is NOT needed?
- A.Everything except the fuel use per 100 km
- B.Only the purchase prices
- C.The purchase prices and the number of vans
- D.The purchase prices, the number of vans and the daily distances
Show the answer
Answer: A. Everything except the fuel use per 100 km
Working
Fuel cost per km = (litres per km) × (price per litre). The price per litre is the same for every type, so the ranking depends only on litres per 100 km: the small van (7) is lowest. Number of vans, daily distance and purchase price do not enter the formula, and the diesel price cannot change the order.
Why the other options are wrong
- B. The number of vans, the daily distances and the diesel price are not needed either: none of them changes the cost per kilometre ranking.
- C. Still keeps the daily distance and the diesel price. Per-kilometre cost does not depend on distance, and one price for all vans cannot change a ranking.
- D. Keeps the diesel price. You would need it to state the cost in euros, but not to rank the types, because it is the same for all of them.
What carries over
A factor shared equally by everything being compared cannot change a ranking.
Question 3: Daily fuel bill for the fleet
Numerical reasoning
A delivery firm's vans
| Van type | Number of vans | Fuel use (litres per 100 km) | Average daily distance per van (km) | Purchase price per van (€) |
|---|---|---|---|---|
| Small | 12 | 7 | 150 | 28,000 |
| Medium | 8 | 9 | 180 | 36,000 |
| Large | 5 | 12 | 120 | 52,000 |
Every van is driven every working day. Diesel costs €1.80 per litre.
What is the firm's total diesel cost for the whole fleet on an average day?
- A.€73.98
- B.€327.60
- C.€460.08
- D.€589.68
Show the answer
Answer: D. €589.68
Working
Litres per day: small ; medium ; large . Total litres. Cost: euros. Check: , minus , gives 589.68.
Why the other options are wrong
- A. This is the cost for one van of each type; it ignores how many vans of each type there are.
- B. 327.6 is the fleet's daily fuel in litres; it still has to be multiplied by €1.80.
- C. Leaves out the large vans, which use 72 litres a day between them.
What carries over
Build a total from its parts with every multiplier the formula needs, then convert to euros once at the end.
Key points
Name the target and its unit, then write the formula before reading the data.
A number with no slot in the formula is superfluous for this question.
A factor that is the same for everything compared cannot change a ranking.
If a slot in the formula cannot be filled, the answer may not be determinable.
All questions here are original and written for UniExamer; none comes from the test maker.
Written by the UniExamer team with AI assistance. Every worked example and check question was re-solved by an independent checker before publication. No subject expert has reviewed this lesson yet. If you find a mistake, write to support@uniexamer.com.