Each of the digits 3. 5. 7, and 8 is written on its own card. The four cards are given to a student, and then the student is asked to use the cards to form the largest three-digit number that is greater than 300 and less than 700. In the number formed, what digit will be in the tens place?
The digit in the tens place will be 8.
To form the largest three-digit number greater than 300 and less than 700 using the digits 3, 5, 7, and 8, the optimal arrangement places 8 in the tens place. This configuration leads to the maximum possible value while adhering to the constraints of the number range.
If 3 were in the tens place, the largest three-digit number that could be formed would be 378, which is less than what can be achieved with 8 in the tens place. Consequently, using 3 in the tens place will not yield the largest possible number.
Placing 5 in the tens place would result in the largest number being 578. While this is a valid option, it is still less than the number that can be formed with 8 in the tens place, which is 873. Therefore, 5 does not maximize the value of the three-digit number.
Using 7 in the tens place allows for the formation of the number 578, which again is less than what is possible with 8 in that position. The digit 7 does not provide the highest three-digit number within the specified range when compared to using 8.
By placing 8 in the tens place, the largest three-digit number formed is 578, which meets the criteria of being greater than 300 and less than 700. This arrangement utilizes the highest digit available in the tens position, optimizing the overall number.
In conclusion, to create the largest three-digit number between 300 and 700 using the digits 3, 5, 7, and 8, positioning the digit 8 in the tens place is essential. This maximizes the value of the number formed, resulting in 578, while ensuring compliance with the specified range. Thus, the tens place digit is confirmed to be 8.
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