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P6 Whole Numbers Questions (with Worked Solutions)

Whole-number operations, place value, and averages from real P6 prelim questions. Every question is from a real Singapore P6 preliminary exam, marked instantly, with step-by-step solutions.

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Example Whole Numbers questions

A few real whole numbers questions from P6 prelim papers. The full set — with marking and progress tracking — is inside SG Maths Exam.

Nanyang 2025 · Paper 2 · Q7 · 3 marks
E, F and G are 2-digit numbers. The average of these 3 numbers is 46. The value of E is 26. The value of F is 7 times the value of G. Find the value of F.
Worked solution
  1. Sum of the 3 numbers $= 46 \times 3 = 138$. $F + G = 138 - 26 = 112$. Since $F = 7G$, $7G + G = 112$, so $8G = 112$, $G = 14$. Then $F = 7 \times 14 = 98$.
Methodist Girls' School (Primary) 2025 · Paper 1 Booklet A · Q11 · 2 marks
Calvin had 20 more stamps than Devi at first. After Devi gave 16 of her stamps to Calvin, Calvin now has 3 times as many stamps as Devi. How many stamps did Devi have at first?
Worked solution
  1. \text{Let Devi have } d \text{ stamps at first
  2. Calvin had } d + 20
  3. \text{After Devi gives 16: Calvin} = d + 36,\ \text{Devi} = d - 16
  4. d + 36 = 3(d - 16)
  5. d + 36 = 3d - 48
  6. 84 = 2d
  7. d = 42
Tao Nan 2025 · Paper 1 Booklet A · Q14 · 2 marks
Lisa packed 60 cream cookies and 75 mint cookies into as many boxes as possible. She packed the same number of each type of cookies in each box. How many mint cookies were there in each box?
Worked solution
  1. \text{HCF}(60, 75) = 15 \text{ boxes}
  2. \text{Mint per box} = 75 \div 15 = 5
St Nicholas 2025 · Paper 1 Booklet A · Q15 · 2 marks
George packed 84 pears and 96 mangoes into as many bags as possible with no fruits left unpacked. He packed the same number of fruits in each bag. The number of each type of fruit in each bag was the same. How many bags of fruits did George pack?
Worked solution
  1. The number of bags is the highest common factor of 84 and 96. $84 = 2^2 \times 3 \times 7$, $96 = 2^5 \times 3$, so $\text{HCF} = 2^2 \times 3 = 12$. George packed 12 bags.
St Nicholas 2025 · Paper 2 · Q3 · 2 marks
At first, the cans in a shop were placed on 60 shelves with an equal number of cans on each shelf. 6 shelves were removed and the cans on these shelves were placed on the remaining 54 shelves. The number of cans on each remaining shelf was 40. How many cans were removed from the 6 shelves?
Worked solution
  1. Total number of cans $= 54 \times 40 = 2160$. At first each of the 60 shelves had $2160 \div 60 = 36$ cans. Cans removed from the 6 shelves $= 6 \times 36 = 216$.
Nanyang 2025 · Paper 1 Booklet B · Q21 · 2 marks
Write down all the common factors of 18 and 45.
Worked solution
  1. Factors of $18$: $1, 2, 3, 6, 9, 18$. Factors of $45$: $1, 3, 5, 9, 15, 45$. Common factors: $1, 3, 9$.

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