Rationale
The digit in the tens place will be 8.
To form the largest three-digit number between 300 and 700 using the digits 3, 5, 7, and 8, we must start with the largest possible hundreds digit that still meets the criteria. In this case, 5 or 7 can be used as the hundreds digit, but to maximize the number, we choose 5 for the hundreds place, followed by 8 in the tens place, making the number 582.
A) 3
If 3 is placed in the tens position, the largest possible number we can create is 375, which is significantly smaller than 582. Thus, this choice does not maximize the three-digit number.
B) 5
Using 5 in the tens place would lead to forming the number 578 if we select 7 for the hundreds place. However, this number is smaller than 582, which is formed by placing 8 in the tens position. Therefore, this option does not yield the largest number.
C) 7
If we place 7 in the tens position, the largest number we can form would be 587, which is again smaller than 582. Thus, this choice does not yield the largest valid three-digit number under the given constraints.
D) 8
Choosing 8 for the tens place, with 5 in the hundreds place and 2 in the units place, gives us the number 582. This is the largest number that can be formed using the digits provided, while also satisfying the condition of being greater than 300 and less than 700.
Conclusion
To maximize the three-digit number within the specified range using the digits 3, 5, 7, and 8, the optimal choice for the tens place is 8. By strategically selecting 5 for the hundreds place and 2 for the units, the largest valid number 582 is achieved, confirming that 8 is indeed the digit in the tens place.
