Some numerical reasoning questions describe a relationship in words; others define an unfamiliar symbol. In both cases, read the definition before calculating. A familiar-looking operation may not be the one the question asks you to perform.
These original examples demonstrate methods for practice, not the specified content or timing of any provider's paper.
Name the quantities first
“Eva has three more counters than Liam” can be represented as E = L + 3. The letters are labels for amounts, not abbreviations to manipulate without meaning.
If Eva has 11 counters, Liam has 8. Adding three to Eva's amount would reverse the relationship. Read your equation back as a sentence to check it against the question.
A drawing or bar model can work just as well as letters during practice. Use the representation your child can explain.
Defined symbols: follow the given rule
Suppose the question defines a ★ b = 2 × a + b. Then 4 ★ 3 = 2 × 4 + 3 = 11.
The star does not mean ordinary multiplication here. Reversing the entries also changes the result: 3 ★ 4 = 10. Do not assume a new operation has the same properties as addition or multiplication.
For (4 ★ 3) ★ 2, calculate the brackets first to get 11, then apply the rule again: 11 ★ 2 = 2 × 11 + 2 = 24.
Rates: compare the same interval
Machine A produces 200 items in five days. Machine B produces 150 items in four days. Both maintain constant average rates with no downtime. How many more items does A produce over eight days?
A's rate is 200 ÷ 5 = 40 items per day, so it produces 320 items. B's rate is 150 ÷ 4 = 37.5 items per day, giving 300 items over eight days. The difference is 20 items.
The 37.5 is an exact average rate, not a rounded whole number. It does not require half a finished item at the end of every day. Keep the average rate exact until calculating the requested interval.
Avoid rounding a rate too early
Alex writes two pages in ten minutes; Brooke writes five pages in fifteen minutes. Assume constant rates and that partial pages count. How much more has Brooke written after twenty minutes?
Alex writes 4 pages. Brooke writes (5/15) × 20 = 20/3 pages, or 6⅔. The difference is 20/3 − 4 = 8/3 pages, or 2⅔ pages.
If a question instead asked for fully completed pages at that point, Brooke would have six and Alex four, a difference of two. These are different questions. Do not round a fractional result to fit an option unless the wording requests that treatment.
Read assumptions as part of the problem
A rate comparison may assume constant speed, equal-sized pages or uninterrupted work. Without an appropriate assumption, a simple proportional calculation may not describe the situation. In a teaching exercise, state the assumption clearly rather than expecting the student to guess it.
Check both interpretation and arithmetic
If your answer does not match any choice, check the relationship, substitution, arithmetic, units and rounding. The mistake is not automatically in the wording step. Sometimes the question or options themselves need correction.
For further practice, explore maths word problems, fractions and percentages and number series. Find sample numerical reasoning through QASMT.