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April 11th, 2018, 12:33 AM   #1
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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 x-y=z,
and x= 100a+10b+c, etc...
but I am not sure about the other parts.

Please help!
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April 11th, 2018, 01:40 AM   #2
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let $X = abc$

Note that $a,c \neq 0$

Then $Y=cba$

$x-y = 100a+10b+c - 100c-10b-a = 100(a-c)+(c-a) = 99(a-c)$

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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