t is a 7-digit even number.there is no repetition of digits.the digit 5 is in in thousands place.the greatest digit is in millions place.the digit in the hundred thousands place is twice the digit in the hundreds place.the digit in the hundreds place is twice the digit in the ones place.the digit in the tens place is 2 less than the digit in the millions place.the value of the digit in the ten thousands place is zero.
7 digits
xxxxxxx
5 in 1000s place
xxx5xxx
greatest digit in millions
9xx5xxx
10s = millions-2
9xx5x7x
10,000s = 0
9x05x7x
100,000s = 2x100s
100s = 2x1s
9805472
9405271
even, so
9805472
To find the 7-digit even number that meets these conditions, let's go step by step:
1. The digit 5 is in the thousands place. Since the number is even, the only even digit that can be in the thousands place is 2.
2. The greatest digit is in the millions place. Since there is no repetition of digits, the greatest digit available is 9. Therefore, 9 is in the millions place.
3. The digit in the hundred thousands place is twice the digit in the hundreds place. Since there is no repetition, the digit in the hundreds place must be half of the digit in the hundred thousands place. The only even digit available is 2, so 4 (twice of 2) is in the hundred thousands place, and 2 is in the hundreds place.
4. The digit in the hundreds place is twice the digit in the ones place. Since there is no repetition, the digit in the ones place must be half of the digit in the hundreds place. The only even digit available is 2, so 4 (twice of 2) is in the ones place.
5. The digit in the tens place is 2 less than the digit in the millions place. Since the value of the tens digit cannot be negative or greater than 9, the only possibility is that the digit in the millions place is 3, and therefore the digit in the tens place must be 1 (3 - 2).
6. The value of the digit in the ten thousands place is zero. Since there is no repetition, the only available digit is 0.
Putting all these digits together according to their positions, we get the 7-digit even number: 9432104.
Therefore, the 7-digit even number that satisfies all the given conditions is 9432104.