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?

Rationale

The digit in the tens place of the largest three-digit number formed is 8.

To find the largest three-digit number greater than 300 and less than 700 using the digits 3, 5, 7, and 8, we start by selecting the highest possible digits for the hundreds and tens places while ensuring the overall number fits the specified range.

A (3) YOUR ANSWER

If 3 is placed in the tens position, the largest possible number would start with 5 or 7 in the hundreds place, leading to numbers like 530 or 730. However, 730 exceeds the limit of less than 700, while 530 is smaller than the maximum possible value of 580, which will not be the largest.

B (5) YOUR ANSWER

Choosing 5 for the tens place limits the hundreds digit to either 3 or 7, resulting in numbers like 350 or 570. While 570 is a valid option, it is still less than the maximum possible combination of 580, which utilizes the digit 8 in the tens place instead.

C (7) YOUR ANSWER

If 7 is in the tens position, the largest possible three-digit number would be 583 (with 5 in the hundreds place). However, this is still not larger than 580, which uses 8 in the tens position and provides a higher overall value.

D (8) CORRECT

Placing 8 in the tens position allows for the largest possible number: 583, when combined with 5 in the hundreds place, or 578 with 7 in the hundreds place. In both cases, 8 being in the tens position is vital for maximizing the value compared to any other digit placement.

Conclusion

In forming the largest three-digit number between 300 and 700 using the digits 3, 5, 7, and 8, the digit in the tens place must be 8 to achieve the maximum value, specifically 580. This ensures that the number remains within the specified range and utilizes the highest available digits effectively.

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?

The digit in the tens place of the largest three-digit number formed is 8.

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