A Five number is divisable by 5 and smaller than 70000. the ten thousand digit is a multiple of three that is greater than 3. The digits in the ten thousands and hundreds place are the same.the sum of the digit in the ones and the thousand is 9.The ones digit is greater than the thousands digit.The digit in the tens place is 3 less than the digit in the thousands place. What is the five digit Number?
To find the five-digit number that satisfies the given conditions, we need to analyze each condition step by step.
Condition 1: The number must be divisible by 5 and smaller than 70000.
To identify the possible range of the number, we can look for numbers that are multiples of 5 below 70000. The two numbers that fit this criteria are 10,000 and 60,000.
Condition 2: The ten thousand digit is a multiple of three that is greater than 3.
Since the ten thousand digit is a multiple of three greater than 3, the only possible digit is 6.
Condition 3: The digits in the ten thousands and hundreds place are the same.
Since the ten thousands and hundreds place digits are the same, we know that the digit is 6.
Condition 4: The sum of the digits in the ones and the thousands place is 9.
Since the sum of the digits in the ones and thousands place is 9, we can try different combinations. The possible combinations are (1, 8), (2, 7), (3, 6), (4, 5), and (5, 4).
Condition 5: The ones digit is greater than the thousands digit.
Since the ones digit is greater than the thousands digit, we can eliminate the combination (4, 5). This leaves us with (1, 8), (2, 7), (3, 6), and (5, 4).
Condition 6: The digit in the tens place is 3 less than the digit in the thousands place.
Using the remaining combinations, we can check if the digit in the tens place is 3 less than the digit in the thousands place.
- For (1, 8): 8 - 3 = 5, which is not 1.
- For (2, 7): 7 - 3 = 4, which is not 2.
- For (3, 6): 6 - 3 = 3, which is correct.
- For (5, 4): 4 - 3 = 1, which is not 5.
Based on the conditions, the five-digit number that satisfies all the given conditions is 63,684.