Teacher shares GCSE maths question most 16-year-olds get wrong – see if you can answer it

Teacher shares GCSE maths question most 16-year-olds get wrong – see if you can answer it A maths question that stumped many students who spent months preparing for their GCSEs – can you figure it out? Unless we ourselves go into teaching, most of us will forget what we learned for our GCSEs within a few years of school. Questions about the Corn Laws or ice age geology come up surprisingly rarely in adult life. But a good grasp of maths always comes in handy. Most of the mathematical challenges we face day-to-day, whether it's working out how many tiles we need for the new bathroom or adapting a cake recipe for a smaller tin than the one Mary Berry uses, can generally be solved easily enough given time, patience, and judicious use of the calculator built into our phones. But it's when we're doing maths under pressure, without the aid of technology, that mistakes can creep in. Secondary school maths teacher Natasha Hall sent us this classic example of a puzzle that's actually easy enough to work out – but also perilously easy to misread. The past AQA exam paper question reads: "A bag contains 72 blue beads and some red beads. Blue beads : red beads = 4:5. Work out the number of red beads." The examinee is being asked to use the proportion of blue to red beads to determine exactly how many red beads are in the bag. But under exam conditions, it's all too easy to get it wrong. Can you work it out? Natasha explains: "Most people read this as meaning that there are 72 beads and so they add up the two ratios and divide 72 by 9 (4 + 5). 72 divides by 9 to give 8 and then 8 × 5 (number of red beads) = 40. However, if you re-read the question it says there are 72 BLUE beads. So the correct method is to divide 72 by 4 (number of blue beads) to get 18 and then multiply 18 × 5 to get the correct answer, 90. There's nothing wrong with the question, but it's easily misinterpreted. Sometimes, though, the mistake is on the paper itself. In June this year, an exam board has apologised after finding mistakes in "all versions" of a GCSE science paper. Tes magazine, the magazine for teachers and school leaders formerly known as the Times Educational Supplement, reported that England's largest exam board, AQA, apologised for the mistake and was forced to report the error to exams regulator Ofqual. Michael Turner, the exam board's chief commercial officer, stressed that AQA "has processes in place to make sure that no learners are disadvantaged by it". He said in the email sent to exams officers: "We're sorry to let you know that there was a mistake on all versions of the GCSE Combined Science Trilogy higher paper 2, which students sat on Monday 15 June 2026." In one of the questions on the paper, students were asked to "calculate the mass of a system", but the answer prompt stated "mass of glider" – which would only make up a portion of the system. It was the second error in a little over a week. Students sitting a foundation-tier GCSE maths paper earlier the same month opened their sealed exam papers to discover that it contained an insert with information intended for another paper. One teacher told Tes that schools had heard nothing from AQA about the incorrect inserts, saying: "In this series of exams we've had two erratum notices for minor typos (geography and physics) but nothing at all for this. Schools only found out via text and email from colleagues working elsewhere. "Exams officers downloaded new inserts and rushed to print them. Some disruption to smooth starts but exams started within the rules - still nothing from AQA now."