Question 1031403: how many numbers between 0 and 100 are divisible by 3 but not by 6
Found 2 solutions by solver91311, MathTherapy:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Let's assume that the question means strictly between 0 and 100, so that 0 and 100 are not included. It really doesn't matter much in the final analysis because neither 0 or 100 is divisible by 3, but just to maintain unambiguous communication we'll keep the assumption.
So that means we are concerned with the set of numbers from 1 to 99, a total of 99 numbers. Since every third number in a consecutive list of numbers is divisible by 3, there must be 33 of these 99 numbers that are divisible by 3. But a number that is divisible by 6 is divisible by both 3 and 2. Hence, we have to toss out every other one of the 33 that are divisible by 3 because every other one is also divisible by 2 and is, therefore, divisible by 6.
So half of 33 is 16 and a half. Whoops! We can't have a fractional result here because the question asks for a number of numbers and expects a whole number result. Therefore, we have to decide whether 16 or 17 is the number divisible by 3 and not divisible by 2, i.e., not divisible by 6.
Since the first "divisible by 3" number in our list is the number 3, which is odd and therefore not divisible by 2, AND the last number in the list that is divisible by 3 is 99 which is also odd and not divisible by 2, we can be certain that 17 of the numbers are divisible by 3 and not by 2.
John
My calculator said it, I believe it, that settles it
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! how many numbers between 0 and 100 are divisible by 3 but not by 6
There are 33 numbers, between 0 ad 100 that're divisible by 3. These numbers are: 3 - 99, inclusive
There are 16 numbers, between 0 ad 100 that're divisible by 3 and 2, or 6. These numbers are: 6 - 96, inclusive.
Numbers between 0 and 100, or specifically: 3 - 99, inclusive, that're divisible by 3 but not 3 and 2 = 33 - 16, or 
|
|
|
