Use all the digits 4, 5, 7, 8 to form(a) the greatest number which is a multiple of 5(b) the smallest number between 5000 and 6000Ans: (a) (b)

1. Break Down the Problem

We need to find:

• (a) The greatest number that can be formed using the digits 4, 5, 7, and 8 which is a multiple of 5.
• (b) The smallest number that can be formed with these digits that lies between 5000 and 6000.

2. Relevant Concepts

For (a), a number is a multiple of 5 if it ends in either 0 or 5. Since we are using the digits 4, 5, 7, and 8, the only digit that can be used at the end to ensure it's a multiple of 5 is 5.

For (b), we need to form a number between 5000 and 6000 using the digits available.

3. Analysis and Detail

1. Finding the Greatest Number Multiple of 5:

   • Since the number must end with 5, we will start by placing 5 at the end.
   • The remaining digits are 4, 7, and 8. To form the greatest number, we should arrange these in descending order.
   • The greatest arrangement would be 874 leading to the final number being 8745.

2. Finding the Smallest Number between 5000 and 6000:

   • The leading digit must be 5 since we are looking for a number between 5000 and 6000.
   • The remaining digits are 4, 7, and 8. To form the smallest number, we should arrange these in ascending order.
   • Thus, the smallest combination will be 5047.

4. Verify and Summarize

• For (a), the greatest number we formed was 8745, and it is a multiple of 5 since it ends in 5.
• For (b), 5047 is within the specified range and uses the digits correctly.

Final Answer

(a) 8745
(b) 5047