Multiple of 8

[ron]

Let N be the greatest integer multiple of 8, no two of those digits are the same. What is the remainder when N is divided by 1000?

[vreddy]

N = 100x+10y+z = 0 (mod 8), where x, y, z are distinct and lie b/w 0 and 9.
Given N is the greatest, hence it should look like 9876543xyz..
<x, y, z> is a permutation of <0, 1, 2>.
Find a permutation, whose numerical equivalent is divisible by 8, from the foregoing set.

Answer is 120.

N = 9876543120

[ron]

Vreddy, you are right. I have seen that you left for awhile and back to solve it. Thanks.

[Leena Pailan]

N = 100x+10y+z = 0 (mod 8), where x, y, z are distinct and lie b/w 0 and 9.
Given N is the greatest, hence it should look like 9876543xyz..
<x, y, z> is a permutation of <0, 1, 2>.
Find a permutation, whose numerical equivalent is divisible by 8, from the foregoing set.

Answer is 120.

N = 9876543120

dear vreddy here are some more questions .can you solve these for me ?
1. the product n of three positive integers is 6 times their sum ,and one of the integers is the sum of the other two . find the sum of all possible values of n.
2. let x and y be positive real numbers such that y^3+y<=x-x^3,prove that y<x<1.
3. let ABCD be aconvex quadrilateral in which <BAC=50 degrees , <CAD=60 degrees , <CBD =30 degrees ,and <BDC=25 degrees . if E is the point of intersection of AC And BD ,find <AEB.