How many numbers between 1 and 100 ?

[tamiri]

How many numbers between 1 and 100 are not divisible by 2 or 3?

My real question is: How many numbers are between 1 and 100?

I figured that there are 49 numbers divisible by 2 [(98-2)/2+1] and
33 numbers divisible by 3 [(99-3)/3+1].
There are 16 numbers divisible by 6 [(96-6)/6+1)]
Hence, 49+33-16= 66 numbers that are divisible by 2 or 3.
Now the trick for me is do I make 99-66=33 or 98-66=32?
I would say there are 98 numbers between 1 and 100 because it does not say "inclusive".
However, in most of suggested answers it says 99 numbers.

Could anyone please explain?

Thanks,
Tamir

[Brent@GMATPrepNow]

How many numbers between 1 and 100 are not divisible by 2 or 3?

My real question is: How many numbers are between 1 and 100?

I figured that there are 49 numbers divisible by 2 [(98-2)/2+1] and
33 numbers divisible by 3 [(99-3)/3+1].
There are 16 numbers divisible by 6 [(96-6)/6+1)]
Hence, 49+33-16= 66 numbers that are divisible by 2 or 3.
Now the trick for me is do I make 99-66=33 or 98-66=32?
I would say there are 98 numbers between 1 and 100 because it does not say "inclusive".
However, in most of suggested answers it says 99 numbers.

Could anyone please explain?

Thanks,
Tamir

Everything looks good.
Since we're dealing with numbers between 1 and 100, we cannot include 1 and 100 in our calculations.
So, there are 98 numbers between 1 and 100.

So, the correct answer is 98 - 66 = 32

Cheers,
Brent

[tamiri]

Thank you Brent for the speedy reply.
Please look at that link :
https://www.beatthegmat.com/numbers-betw ... 29933.html
Are they mistaken?

Thanks,
Tamir

[Brent@GMATPrepNow]

Well, some parts in that link are incorrect, and others are correct. I'll stick by what Ron said,

By default, "between" is exclusive of the stated endpoints of the interval. if the problem writers intend that "between" be inclusive, they'll write "inclusive".

I should mention that we can solve the matter quickly by just listing the values that satisfy the given conditions. In fact, this might even be the fastest approach:
Values that are not divisible by 2 or 3:
5, 7, 11, 13, 17, 19, 23, 25, 29, 31, [10 so far]
35, 37, 41, 43, 47, 49, 53, 55, 59, 61, [20 so far]
65, 67, 71, 73, 77, 79, 83, 85, 89, 91, [30 so far]
95, 97

Altogether, we have 32

Cheers,
Brent