integer problem

Mclaughlin · Posted: Tue May 13, 2008 9:50 pm Post subject: integer problem

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

Where do i begin with this and what are some tips on how to handle questions like this in the future. thanks

arorag · Posted: Tue May 13, 2008 9:57 pm Post subject:

HInt: any no. is divisible by 3 if sum of its digits are divisble by 3
e.q. 102, 105

Mclaughlin · Posted: Tue May 13, 2008 10:05 pm Post subject:

Thanks! great hint. But how do I do this fast without having to list out all the nubmers if I'd rather spend time on harder problems. (if I'm lucky enough to get them)

akshatsingh · Posted: Tue May 13, 2008 11:26 pm Post subject:

200/3 gives 66 and a remainder 2.
hence 66 nos, from 1 to 200 are divisible by 3

100/3 gives 33 and a remainder 1.
hence 33 nos, from 1 to 100 are divisible by 3

So from 100 to 200 there will be 66 - 33 = 33 nos divisible by 3.

My answer is A

shan_shine007 · Posted: Wed May 14, 2008 1:27 am Post subject:

For any no. to be divisible by 3, the sum of the digits of the no. must be divisible by 3.
eg. take 102
sum of digits = 1+0+2 = 3 i.e, divisible by 3
the next no. divisible by 3 is 105 i.e, 3 more than d previous no.

so between 100 & 200 there are 99 integers
hence d no. of integers divisible by 3 between 100 & 200 is
99/3 = 33
ans a

Mclaughlin · Posted: Wed May 14, 2008 6:57 am Post subject:

Thanks both of you! but I have a stupid question. How do you know that there are 99 intergers between 100 to 200. I thought it was 100 intergers.

bia · Posted: Wed May 14, 2008 7:12 am Post subject:

There are 101 integers between 100 and 200. You can use the formula:
((max-min)/distance between two consecutive integer)) +1

We can solve above question much more easily by this formula:

max number divisible to 3 = 198
min number divisible to 3 = 102

So total number between 100 and 200 that is divisible to 3 = (198-102)/3 + 1 = 33

VP_Tatiana · Posted: Wed May 14, 2008 2:58 pm Post subject:

Hi guys,

When a problem asks how many numbers are between two numbers, we want to exclude the endpoints. (Unless it says "inclusive.") So, in this problem we just want to look at the numbers 101-199. You can see that there are there exactly the same amount of numbers as between 1 and 99; there are 99 numbers.

If are examining the numbers between 100 and 200 inclusive, then we also count 100 and 200, and then we have 101 numbers.

In this case, since the endpoints are not divisible by 3, people were able to arrive at the right answer whether they considered the endpoints or not. However, counting the endpoints would have resulted in a wrong answer if the question were "how many numbers divisible by 2 are between 100 and 200?"

Best wishes,

Tatiana

bia · Posted: Wed May 14, 2008 9:27 pm Post subject:

There are ((200-100)/2)+1 = 51 numbers divisible by 2 which are between 100 and 200

Is is right?

shan_shine007 · Posted: Wed May 14, 2008 10:53 pm Post subject:

to find the no. of integers between 100 & 200 ... dont take into account the end pts (100 & 200) ...

So, no, of integers between 100 & 200 = (199- 101)+1= 99