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?

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) (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

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