SOLUTION: the sum of my digits is 12. when rounded off to the nearest hundred. i am 500. rounding the nearest 10 makes me 530. what am i?

Question 1064207: the sum of my digits is 12. when rounded off to the nearest hundred. i am 500. rounding the nearest 10 makes me 530. what am i?
Found 2 solutions by Alan3354, KMST:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
534 or 525
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
There are slight differences
in math definitions from place to place,
so it is important to use the math "dialect"
of the person you are talking to.
As different journals, and/or different disciplines use
different ways to list references in a published paper,
you have to follow the rounding rules of
the author of the problem you posted.

Under the popular and simple rules used where I work right now,
if the digit I am rounding to is followed by
just a 5, or a 5 followed by one or more zeros,
or a 5 followed by 1, 2, 3, or 4,
I must simply round up.
With that rule,
the numbers 123.5, 123.500 and 123.51
are all rounded to 124.

However, I suspect the course this problem comes from
follows a different, more complex, rule.
I have also worked under a different rule,
where a 5 as a dropped digit required looking at
the previous digit, and the next digits.
If there was a non-zero next digit,
the rounding digit was increased,
so that 123.51 was rounded to 124,
and 124.51 was rounded to 125.
If there was no next digit,
or the 5 was followed by zero(s),
the rounding digit was kept as was,
or increased as needed to make it even.
Under that rule, when rounding to the nearest 10,
524 and 525 round down to 520,
while 535 rounds up to 540,
and the numbers 526, 527, ... , 534 round to 530.
Of those numbers, only
has digits that add up to 12.

According to the rounding rules most people use,
there would be more than one solution,
because under those rules
all the numbers from 525 to 534,
including 525 and 534,
round to 530 when rounding to the nearest 10.
Of those numbers,
all of them round to 500 when rounding to the nearest 100, and
for both, 525 and 534, the sum of digits is 12.
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