I’m a 4-digit number. My 1st 2 digits from the left are divisible by 5. My 3rd and 4th digits from the left are divisible by 9. The sum of my digits is 18. Each of my digit is different. I’m divisible by 4. I’m less than 6000. My units digit is twice my tens digit.
just start fitting in the facts.
1st 2 divisible by 5 means they end in 0 or 5
last 2 divisible by 9 and all different means not 09,45,54 or 90
units = twice tens means they are 36
so, the number is xx36.
That means the first two digits also add to 9, which means the number is
4536 or 9036
But the number is less than 5000, so it must be 4536.
To find the number that satisfies all the given conditions, we can go step by step:
Step 1: Start with a list of numbers that are divisible by 5 and have different digits as the first two digits. The numbers in this list can range from 10 to 95, excluding the numbers that have repeating digits (e.g. 11, 22, 33, etc.).
Step 2: Next, consider the third and fourth digits being divisible by 9 and having different digits. The numbers in this list can range from 18 to 99, again excluding any numbers with repeating digits.
Step 3: Now, check if the sum of the digits is 18. For example, if the first two digits are 45, then the remaining digits would be 9 and 9, making the sum of the digits 45 + 9 + 9 = 63, which is not equal to 18. Continue this process for all possible combinations from Step 1 and 2.
Step 4: Among the numbers that satisfy the previous conditions, check which ones are divisible by 4. Remember, in order to be divisible by 4, the number formed by the last two digits must be divisible by 4. For example, if the last two digits are 18, then the number would be 4518. Only consider the numbers that are less than 6000.
Step 5: Finally, among the remaining numbers, check if the units digit is twice the tens digit. For example, in the number 4518, 1 is not twice 8, so it does not satisfy this condition.
Continue this process until you find a number that satisfies all the given conditions.