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April 11th, 2018, 12:33 AM  #1 
Member Joined: Apr 2018 From: On Earth Posts: 34 Thanks: 0  Digits represented by x,y,z
X is a three digit number. When its digits are reversed, it becomes the three digit number y. The difference between x and y is z, where z is positive and its last digits is 4. Find the numerical value of z. So I know that xy=z, and x= 100a+10b+c, etc... but I am not sure about the other parts. Please help! 
April 11th, 2018, 01:40 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,091 Thanks: 1087 
let $X = abc$ Note that $a,c \neq 0$ Then $Y=cba$ $xy = 100a+10b+c  100c10ba = 100(ac)+(ca) = 99(ac)$ The only multiple of $99$ that ends in $4$ is $594$ and thus $z=594$ Note there are a variety of 3 digit numbers that produce this result, but 594 is always the positive difference that ends in 4. 

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