The answer
\(229\) letters
PSLE 2022 Paper 1 Question 29 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 29 of the PSLE 2022 Paper 1 Mathematics paper. It tests number patterns, in the Number & Algebra strand. It is worth 2 marks. Open your copy of the paper at this question, then follow our full worked solution below.
The pattern repeats every 5 letters: A B A C A (3 A's per set). \(137 \div 3 = 45\) r \(2\): after 45 sets (\(225\) letters) there are 135 A's. The 136th A is the 1st letter of the next set and the 137th A is its 3rd letter; the 4th letter (C) can still be written without adding another A, but the 5th (A) cannot. Greatest number of letters \(= 225 + 4 = 229\).
Answer: \(229\) letters
Same structure, different costume
Change egg tarts to badges, a tank to two tanks, a ring of card to a folded sheet, and a child sees a brand new problem. The lock underneath is the same, and so is the key. Once a student can name the structure, a whole row of questions that look different start to open the same way.
It is also where marks really leak. Across fourteen years of papers, the marks lost in PSLE math leak at the reading far more than at the arithmetic, which is exactly why recognising the structure fixes them. We call this Lock and Key: name the lock, then the key follows.
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One of the 10 question types
The PSLE keeps testing the same 10 structures. Our PSLE Math Intensive trains the Lock and Key reflex across all ten, with 158 curated questions over two days.
It is a number patterns question from the Number & Algebra strand, worth 2 marks.
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