Number PlayClass 8 Mathematics Case Study Questions
10 Questions
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Case 1 of 10
Case Study7 marks
The Library Book Donation
Ms. Anjali, the librarian at a city school, receives a large donation of books for the new library wing. After counting, she finds the total number of books is a 4-digit number represented as
6a2b, where a and b are missing digits. She recalls the donor mentioning two interesting facts: the total number of books is perfectly divisible by 9, and also perfectly divisible by 4. She needs to find the exact number of books to update her inventory records before arranging them on the shelves.Questions on this case
1(1 mark)MCQ
For the number
6a2b to be divisible by 4, which part of the number must be divisible by 4?2(1 mark)
Based on the divisibility rule for 4, what are the possible values for the digit
b?3(1 mark)MCQ
The total number of books is also divisible by 9. What is the divisibility rule for 9?
4(2 marks)
Using the divisibility rule for 9, find the value of
a if b=4.5(2 marks)
Considering all conditions, find all possible 4-digit numbers for the total books.
Case Study6 marks
The Secret Clubhouse Code
Rohan and his friends built a clubhouse and secured the door with a digital lock. To make it fun, they used a cryptarithm puzzle as the code. The puzzle is a multiplication problem:
GH × H = 9K. In this puzzle, G, H, and K are distinct (different) digits from 0 to 9. To enter the clubhouse, a member must solve the puzzle and find the values of G, H, and K. The final code for the lock is the 3-digit number GHK.Questions on this case
1(1 mark)MCQ
The product
GH × H results in a 2-digit number 9K. What does this tell you about the possible range for the digit H?2(1 mark)
Looking at the units digit of the multiplication
GH × H = 9K, the product of H × H must result in a number that ends with the digit K. What happens if H=4?3(2 marks)
Assuming H=4 and K=6, the equation becomes
G4 × 4 = 96. What is the value of G?4(1 mark)MCQ
Do the values G=2, H=4, and K=6 satisfy all the conditions of the puzzle?
5(1 mark)
What is the 3-digit code
GHK for the digital lock?Case Study7 marks
The Community Garden Riddle
Mr. Sharma, a retired mathematics teacher, is in charge of a community garden. He has a number of rose saplings to plant. He tells the young volunteers a riddle: "I have some saplings, fewer than 150. When I try to group them in 3s, one sapling is left over. When I group them in 5s, one is still left over. But when I group them into 7s, they form perfect groups with none left over. Can you figure out how many saplings I have?"
Questions on this case
1(1 mark)MCQ
The number of saplings, N, is a multiple of 7. Which of the following numbers could be N?
2(1 mark)
The number of saplings N leaves a remainder of 1 when divided by 5. What does this tell us about the units digit of N?
3(2 marks)
List all the multiples of 7 that are less than 150 and also have a units digit of 1 or 6.
4(2 marks)MCQ
The final condition is that N leaves a remainder of 1 when divided by 3. Which of the numbers from the previous step satisfies this condition?
5(1 mark)
What is the total number of saplings Mr. Sharma has?