The question is below
Suppose x and y are 2 integers and that $0< x < y < 10 $. The tenths digit of the decimal representation of $x/16$ is $5$. What is the hundredths digit of $17/y$ ?
I was able to solve the above answer (8). But i had to go through each and every integer between 0-10. The answer along with explanation used below strategy which i could not understand.
Since the tenths digit of the decimal version of $x/16$ is 5, x must have a value of at least half of 16. That is, $x>=8$ .....
I do not understand above bold statement, can somebody explain ? why x must have a value of atleast half of 16 if the tenths digit of decimal version of x/16 is 5.
Above is crucial to understand as it speeds up the process of answering. Thanks.
$8/16 = 0,5$ - there is your 5 in the tenth digit's place of decimal representation
Anything below 8/16 will not have 5 as the first digit of decimal representation, since for any natural $ n < 8, n/16 < 8/16 = 0,5$, which means, that there will no longer be digit 5, but digit 4 (for instance, $7/16 = 0,4375$) or even less, down to digit 0 ($1/16 = 0,0625$)