SOLUTION: I am more than 100 but less than 200. I am divisible by 5. The sum and product of my digits are divisible by 5. My three digits are odd. Which number am I?

Algebra ->  Proofs -> SOLUTION: I am more than 100 but less than 200. I am divisible by 5. The sum and product of my digits are divisible by 5. My three digits are odd. Which number am I?      Log On


   

Question 582293: I am more than 100 but less than 200. I am divisible by 5. The sum and product of my digits are divisible by 5. My three digits are odd. Which number am I?
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!

_ _ _

The first digit has to be 1 since it's more than 100 but less than 200.
So it's

1 _ _


Since it's divisible by 5 the last digit is either 0 or 5.
Since the three digits are odd, the last digit can only be 5.
So it's

1 _ 5

Now we are certain that the product of the digits will be a multiple
of 5.

Since the sum of those two digits is 6 and the sum of the digits 
is a multiple of 5, that multiple of 5 could only be 10 or 15,
which would require the middle digit to be 4 or 9.  But since
the digits are all odd, it can't be 4, so it has to be 9.  So the 
number is

1 9 5

Edwin