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How many multiples of 3 are there between 9 and 99 inclusive

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Director
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Joined: 25 Oct 2008
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Location: Kolkata,India
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Kudos [?]: 178 [0], given: 100

How many multiples of 3 are there between 9 and 99 inclusive [#permalink] New post 16 Jul 2009, 21:06
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How many multiples of 3 are there between 9 and 99 inclusive?
options:30 31 32 33 34
Ans 31

Here's where I am getting stuck:
3 x 3 =9
3 x 33 =99
Since the question asks for "including" there are 33-3+1=31 numbers.The solution ends here,but I went furthur and substracted 2 more (for 3x1 and 3x2.ofcourse because such an option was notthere I realised my mistake and "guessed the correct answer.)
Can somebody tell me when the last step is reqd.?Because I clearly remember doing such a problem where the last step was reqd.!
Thnx!
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Kudos [?]: 99 [0], given: 15

Re: How many multiples of 3 are there between 9 and 99 inclusive [#permalink] New post 16 Jul 2009, 21:27
The last step would be required when you do not divide 9 and 99 by 3 to get 3 and 33.

When you subtract 3 from 33, you are actually not eliminating the number 3 itself from 33, but you are eliminating the 1st 3 multiples of 3 (ie, 3, 6 and 9) from all the multiples upto 99.
What you did wrong was that first you subtracted 3 from 33, (ie, you removed 3,6 & 9 from 9 - 99) and then again you removed 3 and 6.
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Director
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Re: How many multiples of 3 are there between 9 and 99 inclusive [#permalink] New post 16 Jul 2009, 21:54
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Actually this is not supposed to be so complicated !
consider 1 to 99 inclusive -> how many multiples of 3 are there? 99/3 = 33 . Now remove 3 and 6
Ans 31.
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Re: How many multiples of 3 are there between 9 and 99 inclusive [#permalink] New post 16 Jul 2009, 22:08
Expert's post
to avoid mistakes I always used formula N = (max-min)/k + 1
where max and min are maximum and minimum divisible numbers.
For example,
9..99 -- > N = (99-9)/3 + 1 = 31
8..98 -- > N = (96-9)/3 + 1 = 30
10..101 -- > N = (99-12)/3 + 1 = 30
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Re: How many multiples of 3 are there between 9 and 99 inclusive   [#permalink] 16 Jul 2009, 22:08
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