Question

Use the digits 4, 5, 6, and 7 to create two 3-digit numbers where the sum is between 1,000 and 1,100, and the difference is less than 100. Explain your thinking!!

A) 645, 467
B) 754, 356
C) 547, 463
D) 657, 431

Answer 1

To create two 3-digit numbers where the sum is between 1,000 and 1,100 and the difference is less than 100 using the digits 4, 5, 6, and 7, we can consider the possible combinations: 645 and 467, 754 and 356, 547 and 463, 657 and 431. Only the combination of 547 and 463 satisfies the conditions.

Step-by-step explanation:

To create two 3-digit numbers where the sum is between 1,000 and 1,100, and the difference is less than 100 using the digits 4, 5, 6, and 7, we can consider the possible combinations:

1. 645 and 467: The sum is 645 + 467 = 1,112, which is outside the specified range.
2. 754 and 356: The sum is 754 + 356 = 1,110, which is within the specified range. The difference is 754 - 356 = 398, which is greater than 100, so this combination doesn't meet the requirements.
3. 547 and 463: The sum is 547 + 463 = 1,010, which is within the specified range. The difference is 547 - 463 = 84, which is less than 100, so this combination satisfies the conditions.
4. 657 and 431: The sum is 657 + 431 = 1,088, which is within the specified range. The difference is 657 - 431 = 226, which is greater than 100, so this combination doesn't meet the requirements.

Therefore, the only combination that satisfies the conditions is 547 and 463 (option C).