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# determining the number of multiples in a range

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Director
Joined: 23 Apr 2010
Posts: 538
determining the number of multiples in a range  [#permalink]

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02 Feb 2011, 02:48
I would like to ask to clarify the following issue for me:

How many numbers between 10 and 100 are multiples of 2, 3, 5, 6?

My approach for multiples of 2:
numbers_between_10_and_100 = 100 - 10 + 1 = 91
#_multiples = 91/2 = 45.5

And now I don't know whether I should take 45 or 46?

Thank you.
Math Expert
Joined: 02 Sep 2009
Posts: 55639
Re: determining the number of multiples in a range  [#permalink]

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02 Feb 2011, 03:06
2
4
nonameee wrote:
I would like to ask to clarify the following issue for me:

How many numbers between 10 and 100 are multiples of 2, 3, 5, 6?

My approach for multiples of 2:
numbers_between_10_and_100 = 100 - 10 + 1 = 91
#_multiples = 91/2 = 45.5

And now I don't know whether I should take 45 or 46?

Thank you.

You are applying wrong formula.

$$# \ of \ multiples \ of \ x \ in \ the \ range = \frac{Last \ multiple \ of \ x \ in \ the \ range \ - \ First \ multiple \ of \ x \ in \ the \ range}{x}+1$$.

How many multiples of 4 are there between 12 and 96, inclusive?

Last multiple of 4 IN the range is 96;
First multiple of 4 IN the range is 12;

$$\frac{96-12}{4}+1=22$$.

OR: how many multiples of 5 are there between -7 and 35, not inclusive?

Last multiple of 5 IN the range is 30;
First multiple of 5 IN the range is -5;

$$\frac{30-(-5)}{5}+1=8$$.

OR: How many multiples of 7 are there between -28 and -1, not inclusive?

Last multiple of 7 IN the range is -7;
First multiple of 7 IN the range is -21;

$$\frac{-7-(-21)}{7}+1=3$$.

Check for practice:
good-one-99697.html
3-digit-numbers-divisible-by-7-and-others-81895.html
beginner-s-forum-question-106168.html
multiple-of-105318.html
number-system-103779.html
even-multiples-of-15-between-295-and-101810.html
m01-question-79061.html
m16-74052.html
multiples-98997.html
gmat-club-m16-95744.html
odd-multiples-of-94877.html
totally-basic-94862.html

Hope it helps.
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Director
Joined: 23 Apr 2010
Posts: 538
Re: determining the number of multiples in a range  [#permalink]

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02 Feb 2011, 03:11
1
Thanks a lot, Bunuel.
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Joined: 09 Sep 2013
Posts: 11377
Re: determining the number of multiples in a range  [#permalink]

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12 Sep 2018, 14:46
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Re: determining the number of multiples in a range   [#permalink] 12 Sep 2018, 14:46
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