SOLUTION: iam a 3 digit number less than 300 iam divisible by 2 and 5 but not 3 the sum of my digits is 7 what number am i.

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Question 247337: iam a 3 digit number less than 300 iam divisible by 2 and 5 but not 3 the sum of my digits is 7 what number am i.
Found 2 solutions by solver91311, Edwin McCravy:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


Numbers that are divisible by 5 have a last digit of either 0 or 5. Numbers that are divisible by 2 are even numbers. Since any number that ends in 5 is not an even number, the number we are looking for must end in 0. Numbers that are divisible by 3 have a sum of digits that is divisible by 3. Since 7 is not divisible by 3, any number that qualifies by the fact that the sum of the digits is 7 also qualifies on non-divisibility by 3. Since this is a 3-digit number less than 300, the hundreds digit must be either 1 or 2. 7 minus 1 is 6, so one possibility is 160. 7 minus 2 is 5 so the other possibility is 250.


John
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!

Since the number is to be divisible by both 2 and 5 it is 
divisible by 10. Therefore it ends in a 0.  So the sum of 
its digits are just the sum of the first two digits. Since 
it has to be less than 300, the first digit can only be 
1 or 2. We just need to find two digits whose sum is 7, with
the first one 1 or 2.  1 and 6 have sum 7, and 160 is not 
divisible by 3.

So one answer is 160.

But also 2 and 5 have sum 7, and 250 is not divisible by 3. 

So the other answer is 250. 

They didn't need to tell us it isn't divisible by 3, because
it couldn't be anyway.

Edwin
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