How many natural numbers N have the property among 1,2,,N exactly 30% are divisible by 3? A. 0
B. 2
C. 6
D. infinite

The answer is B. 2.

Step-by-step explanation:

We know that for N = 1 and N = 2, none of them are divisible by 3.

For N = 3, 33.33% are divisible by 3.  For N = 4, 25% (which is already less than 30%), so N = 5 would also be less.

At N = 6, we're back up to 33.33%.  N = 7 is already less than 30%.

At N = 9, you guessed it, 33.33%.  N = 10 is 30% (3, 6, and 9).  So we have one case.

Moving along, at N = 18, 33.33%.  N = 20 is again 30% (3, 6, 9, 12, 15, and 18).  Two cases now.

Finally, at N = 21, again 33.33%.  N = 22 and N = 23 are both greater than 30%.  As we continue this, for any N after 20, we will always be greater than 30%.

21

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need more info

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