Problem Solving and Quantitative Reasoning
What you must understand
This domain tests multi-step reasoning: translating a word problem into operations, identifying relevant information, working backwards, and checking answers. Candidates should be able to use unitary method, work-rate problems, and logical deduction, and to decide which operation a situation requires.
Traps to watch for
- Irrelevant data: questions often include numbers you do not need; identify the goal first.
- Hidden two-step structure: a question may require a subtraction then a division, e.g. finding cost per item after a discount.
- Work-rate addition: if one worker takes 6 hours and another 3 hours, together they take 1 ÷ (1/6 + 1/3) = 2 hours, not the average of 6 and 3.
- Unit mismatch: ensure all quantities share units before combining.
- Answering the wrong question: re-read to confirm whether it asks for the total, the difference, or the rate.
Worked example
A shop sells pens at 3 for £1.20. How much do 7 pens cost? Unitary method: one pen costs £1.20 ÷ 3 = £0.40. Seven pens cost 7 × £0.40 = £2.80.
Rule of thumb: restate the question in your own words, list the given facts, and work step by step, checking at the end that the answer is sensible in context.