A four-digit number between 12 and 13 has an odd number in the hundredths place and an even number in the tenths digit. The sum of the tenths and hundredths digit is 9. What are the possible four-digit numbers?
12. _ _
12.27
12.45
12.63
12.81
12.09
To find the possible four-digit numbers that satisfy the given conditions, we need to analyze the problem step by step.
1. The number is between 12 and 13: This means that the thousands place must be 1.
- So, the number is in the format 1 _ _ _
2. The number has an odd number in the hundredths place: This means that the hundredths place can only be 1, 3, 5, 7, or 9.
- The number possibilities are: 1 1 _ _, 1 3 _ _, 1 5 _ _, 1 7 _ _, and 1 9 _ _
3. The number has an even number in the tenths place: This means that the tenths place can only be 2, 4, 6, or 8.
- By examining the possibilities from step 2:
- The number 1 1 _ _ does not satisfy this condition since there is 1 in the tenths place. (Odd)
- The number 1 3 _ _ satisfies this condition since there is 3 in the hundredths place and 2 in the tenths place.
- The number 1 5 _ _ satisfies this condition since there is 5 in the hundredths place and 4 in the tenths place.
- The number 1 7 _ _ does not satisfy this condition since there is 7 in the tenths place. (Odd)
- The number 1 9 _ _ satisfies this condition since there is 9 in the hundredths place and 8 in the tenths place.
4. The sum of the tenths and hundredths digits is 9: This means that the sum of the remaining digits (ones and thousands places) must be 9.
- The possibilities are:
- For the number 1 3 _ _: 1 3 4 1 (3 + 4 = 7) and 1 3 5 1 (3 + 5 = 8).
- For the number 1 5 _ _: 1 5 4 9 (5 + 4 = 9).
Therefore, the possible four-digit numbers that satisfy all the given conditions are: 1341, 1351, and 1549.