SOLUTION: What number am I? I am a three-digit number. I am less than 200. I am divisible by 12, and by 9. My units digit is less than my tens digit.

Question 248342: What number am I?
I am a three-digit number.
I am less than 200.
I am divisible by 12, and by 9.
My units digit is less than my tens digit.
Found 2 solutions by jim_thompson5910, richwmiller:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let's list all of the multiples of 12 until we hit 200:

0, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192

Let's list all of the multiples of 9 until we hit 200:

0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198

Now let's list all of the multiples of BOTH 12 and 9 until we hit 200:
0, 36, 72, 108, 144, 180

Of those multiples, only 108, 144, and 180 are 3 digit numbers. The only number that has a units digit less than its tens digit is 180.

So the unknown number is 180.
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
let x=number
100a+10b+c=x
I am a three-digit number.
I am less than 200.
This tells me that the digit for hundreds is 1
It is a three digit number less than 200
Three digits numbers start with 100
so a=1
I am divisible by 12, and by 9.
divisible by 12
108, 120, 132, 144, 156,168,180,192
My units digit is less than my tens digit.
120, 132,180 and 192
divisible by 9
180

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