I'm embarassed I can't figure this out

[Mclaughlin]

What is the total number of integers between 100 and 200 that are divisible by 3?
(A) 33
(B) 32
(C) 31
(D) 30
(E) 29


OA is A but I think it's B. can someone tell me why it's A. I got A but then subtracted one because 100 and 200 are even.
GRRR.

[john1234]

It is 33. 200-100 = 100 .So the 100/3 =33,reminder 1. If the first and the last number is divisible by 3,you will just add 1 to what u get after division.

Hope this help.

[egybs]

It is 33. 200-100 = 100 .So the 100/3 =33,reminder 1. If the first and the last number is divisible by 3,you will just add 1 to what u get after division.

Hope this help.

If the range given had been 100-201... using your method you'd get 101/3 which is equal to 33.666 while there would be 34 numbers divisible by 3.... you'd need to add one if either the first or last, or both numbers were divisible by 3. But this only works for divis by 3.

The full way to do it would be something like as follows:

First figure out the range of numbers that are divis by 3... in this case it would be: 102 - 198... It might be tempting to just subtract and divide by three, but you'd be missing out on one.

I find it helpful to firstly divide both of the numbers by 3. So 102/3 is 34 and 198/3 is 66.

Now you want to figure out how many numbers are between 34 and 66. Here's a little trick. Instead of subtracting 34 from 66.. Subtract whatever number from both that changes the lower number into 1. So in this case, subtract 33 from both and you get 1 and 33. This gives you 33.

[raunekk]

Now you want to figure out how many numbers are between 34 and 66. Here's a little trick. Instead of subtracting 34 from 66.. Subtract whatever number from both that changes the lower number into 1. So in this case, subtract 33 from both and you get 1 and 33. This gives you 33



Hi egybs..

I found ur method interesting.. but getting a bit confused..

Can u please elaborate a bit...

thx a lot

[/quote]

[egybs]

Sure...

When trying to find how many digits are between two different numbers a little trick that I like (but is by no means necessary) is to change the range to 1 to X.


So let's say we want to figure out how many integers are between -32 and 100, inclusive. We'll want to change the range -32 - 100 to 1 - something. In this case, we'll add 33 to both numbers since -32+33 = 1. So we now end up with a new range of 1 - 133. How many numbers is this? Start counting: 1, 2, 3,4.... and you'll quickly realize that the answer is 133.

Now this is just the same thing as doing 100 - (-32) = 132 and then adding 1. But this ends up being faster for me.