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Mathematics
Advanced Problem Solving in Class 6 Mathematics
Place Value, Rounding, Estimation, and Multi-Step Computation
100 pts
10 questions • ~35 min
Read each question carefully and answer to the best of your ability. Show all working for word problems.
1.
10 pts
Word Problem
Given the number 623541, determine the difference between the place value of the digit 6 and the place value of the digit 5. Then, express your answer in the Indian numbering format.
Working:
Answer:
Worked Solution:
Step 1: Identify the place value of 6, which is in the hundred-thousands place (6 × 1,00,000 = 6,00,000).
Step 2: Identify the place value of 5, which is in the hundreds place (5 × 100 = 500).
Step 3: Compute the difference: 6,00,000 - 500 = 5,99,500.
Answer: 5,99,500
2.
10 pts
Word Problem
Using the digits 6, 0, 8, 4, and 1, form the greatest possible 6-digit number by allowing one digit to be repeated. Explain your reasoning and show each step.
Working:
Answer:
Worked Solution:
Step 1: Arrange the given digits in descending order: 8, 6, 4, 1, 0.
Step 2: Since only 5 distinct digits are available and a 6-digit number is required, repeat the highest digit (8) to maximize the number.
Step 3: Place the repeated digit in the highest place value positions to form the number: 8, 8, 6, 4, 1, 0.
Answer: 886410
3.
10 pts
Word Problem
Determine how many unique 4-digit numbers can be formed using the digits 3, 4, 9, and 0, ensuring that the number does not start with 0. Provide a detailed explanation of your process.
Working:
Answer:
Worked Solution:
Step 1: Recognize that the thousands place cannot be 0; therefore, possible digits for the thousands place are 3, 4, and 9 (3 options).
Step 2: For each valid thousands digit, the remaining 3 digits can be arranged in 3! = 6 ways.
Step 3: Multiply the possibilities: 3 × 6 = 18.
Answer: 18
4.
10 pts
Word Problem
Two petrol tanks contain 6325 ℓ and 4890 ℓ respectively. Estimate the difference in petrol between the two tanks by first rounding each volume to the nearest hundred litres. Provide all working steps.
Working:
Answer:
Worked Solution:
Step 1: Round 6325 ℓ to the nearest hundred: 6325 → 6300 ℓ.
Step 2: Round 4890 ℓ to the nearest hundred: 4890 → 4900 ℓ.
Step 3: Compute the estimated difference: 6300 ℓ - 4900 ℓ = 1400 ℓ.
Answer: 1400 ℓ
5.
10 pts
Word Problem
Estimate the product of 958 and 387 by rounding each factor to the nearest hundred. Show all steps in your estimation process.
Working:
Answer:
Worked Solution:
Step 1: Round 958 to the nearest hundred: 958 → 1000.
Step 2: Round 387 to the nearest hundred: 387 → 400.
Step 3: Multiply the rounded numbers: 1000 × 400 = 400000.
Answer: 400000
6.
10 pts
Word Problem
Estimate the quotient of 2838 divided by 125 by rounding both the dividend and the divisor to the nearest hundred. Provide detailed working for your estimation.
Working:
Answer:
Worked Solution:
Step 1: Round 2838 to the nearest hundred: 2838 → 2800.
Step 2: Round 125 to the nearest hundred: 125 → 100.
Step 3: Perform the division with the rounded numbers: 2800 ÷ 100 = 28.
Answer: 28
7.
10 pts
Word Problem
A school management spent $26,756 on teachers' pay, $325,378 on building construction, $5,780 on games, and $8,235 on other work. Calculate the total expenditure, showing each step and using the Indian numbering style where appropriate.
Working:
Answer:
Worked Solution:
Step 1: Sum the amounts: 26756 + 325378 = 352134.
Step 2: Add the next amount: 352134 + 5780 = 357914.
Step 3: Add the final amount: 357914 + 8235 = 366149.
Answer: 3,66,149
8.
10 pts
Word Problem
Madhu had $9031. After buying a TV, she was left with $1356. Determine the amount she paid for the TV, and provide each step of your calculation.
Working:
Answer:
Worked Solution:
Step 1: Subtract the remaining amount from the initial amount: 9031 - 1356.
Step 2: Perform the subtraction: 9031 - 1356 = 7675.
Answer: 7675
9.
10 pts
Word Problem
A country's population in 1990 was 906450600. In 1991, the population increased by 9889700. Calculate the population in 1991 with clear working steps.
Working:
Answer:
Worked Solution:
Step 1: Write down the initial population: 906450600.
Step 2: Add the increase: 906450600 + 9889700.
Step 3: Compute the sum: 906450600 + 9889700 = 916340300.
Answer: 916340300
10.
10 pts
Word Problem
Combine two computations: First, find the sum of the predecessor of 97801 and 90526. Second, calculate the product of the successor of 147 and 389. Finally, add both results together. Provide detailed, step-by-step working.
Working:
Answer:
Worked Solution:
Step 1: Find the predecessor of 97801, which is 97800.
Step 2: Compute the sum with 90526: 97800 + 90526 = 188326.
Step 3: Find the successor of 147, which is 148.
Step 4: Multiply 148 by 389: 148 × 389. (This can be computed as: 148 × 400 = 59200, and 148 × 11 = 1628, so 59200 - 1628 = 57572.)
Step 5: Add the two results: 188326 + 57572 = 245898.
Answer: 245898
10
Total Questions
100
Total Points
~35
Minutes