Homework Help: math

Posted by Anonymous on Wednesday, September 21, 2011 at 9:54pm.

It is less than 100,000. it's an even number. it is divisible by 2,3, and 6. None of the digits is less than 4. None of the digits is used more than once. the sum of the digits is 30. The digit in the hundreds place is 2 less than the digit in the thousands place. The digit in the ten-thousands place is one more than the digit in the thousands place. The digit in the tens place is one less than the digit in the hundreds place. If the number were increased by 6, it would be divisible by 2,3,4,6, and 9. Find the number.

math - Steve, Thursday, September 22, 2011 at 5:05pm
Number is abcde
a+b+c+d+e = 30
c=b-2
a=b+1
d=c-1

b+1 + b + b-2 + b-3 + e = 30
4b + e = 34
e is 4,6,8
4b = 30,28,26
so, b=7

Number is a7cd6 = 87546 = 2*3*14591
Adding 6, we get 87552 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 * 19

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