34. 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 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?
Answer: D
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 student should prioritize the highest digits available for the hundreds and tens places. Given the constraints, the largest valid number is 583, where 8 occupies the tens place.
A) 3
Choosing 3 for the tens place would imply a lesser number than 583, as the largest three-digit number with 3 in the tens place could only be 370 or lower, which does not maximize the value of the number formed. Therefore, this option is incorrect.
B) 5
While 5 could be positioned in the tens place, the largest number possible would then be 578. Although this is a strong candidate, it is not as large as 583, which uses 8 in the tens place. Thus, this option does not yield the maximum number.
C) 7
If 7 were in the tens place, the largest number possible would be 578. However, this again does not maximize the usage of the available digits as effectively as using 8 would, hence failing to achieve the largest possible value.
D) 8
Placing 8 in the tens position allows the formation of the number 583, which is indeed the largest three-digit number that fits the criteria of being greater than 300 and less than 700. This option is correct.
Conclusion
The correct answer is 8, as it enables the creation of the largest valid three-digit number, 583, under the specified conditions. All other options fail to maximize the number effectively based on the given digits, resulting in lower values that do not fulfill the requirement of being the largest number within the given range.