Question

A shoe seller has 1000 shoes in his shop. He wants to arrange them in a rack in such a way that the number of rows and columns remains the same. What is the minimum number of shoes he needs more for this purpose?

• A. 24
• B. 32
• C. 34
• D. 14

Hint:

For arranging items in a square, find the closest perfect square number greater than or equal to the total count.
The difference is the number of items needed to make a perfect square arrangement.

Answer 1

The Correct Option is A

The seller wants to arrange the shoes in a rack such that the number of rows equals the number of columns. This means the total number of shoes should be a perfect square number.
Step 1: Identify the perfect squares near 1000
- $31^2 = 961$ (less than 1000)
- $32^2 = 1024$ (just above 1000)
Step 2: Calculate additional shoes needed
To have a perfect square, the seller needs to have 1024 shoes.
Additional shoes required = $1024 - 1000 = 24$
Step 3: Conclusion
So, the minimum number of shoes he needs more is 24.