A three-digit number satisfies the following conditions: The digits are consecutive whole numbers in increasing order; the sum of each pair of digits is greater than 14 and less than 18; and the tens digit is an even number. what is the number
From the given conditions, we can deduce that the tens digit must be 2, since it is the only even number between 0 and 9.
Let's consider the hundreds digit. Since the digits are consecutive whole numbers in increasing order, the only possibility for the hundreds digit is 1.
Finally, we need to find the units digit. The sum of each pair of digits is greater than 14 and less than 18. In this case, the only combination that satisfies this condition is 1 + 2 = 3.
Therefore, the number is 123.
To find the three-digit number that satisfies the given conditions, we can go through each possibility step by step.
1. According to the conditions, the digits should be consecutive whole numbers in increasing order. So, the possible options for the tens digit are 2, 4, 6, or 8.
2. Next, let's consider the sum of each pair of digits. The sum must be greater than 14 and less than 18.
- If the tens digit is 2, the possible units digit can be 3 (2 + 3 = 5) or 4 (2 + 4 = 6).
- If the tens digit is 4, the possible units digit can be 5 (4 + 5 = 9) or 6 (4 + 6 = 10).
- If the tens digit is 6, the possible units digit can be 7 (6 + 7 = 13) or 8 (6 + 8 = 14).
- If the tens digit is 8, there are no consecutive whole numbers that satisfy the condition, as the highest possible units digit would be 9, resulting in a sum greater than 14.
3. Since the tens digit must be an even number, the only valid options for the tens digit are 2, 4, or 6.
- If the tens digit is 2, the number can be 23 or 24.
- If the tens digit is 4, the number can be 45 or 46.
- If the tens digit is 6, the number can be 67 or 68.
4. Based on the possible options, the valid three-digit number that satisfies all the given conditions is 67.
Therefore, the number is 67.