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# How to find numbers inbetween set

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Manager
Joined: 13 Jun 2016
Posts: 118
Location: United States
Concentration: Finance, Technology
How to find numbers inbetween set  [#permalink]

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20 Apr 2017, 20:47
Is there a formula to quickly figure out the number of numbers between lets say -40 to 100 that are divisible by 3?
Intern
Joined: 30 Mar 2017
Posts: 3
How to find numbers inbetween set  [#permalink]

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24 Apr 2017, 13:07
Yeah

The first number divisible by 3 in your set would be -39 and the last would be 99
step 1: subtract largest divisible number in set by the smallest: 99 - (-39) = 138
step 2: divide the difference by the divisible number: 138 / 3 = 46
step 3: add 1: 46 + 1 = 47 total numbers between 99 and -39 that are divisible by 3

This is easy to see with small numbers
For example:
set = from 7 to 21, we need to find number of numbers divisible by 7
21- 7 = 14
14 / 7 = 2
2 + 1 = 3
Current Student
Joined: 17 Jun 2016
Posts: 515
Location: India
GMAT 1: 720 Q49 V39
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WE: Engineering (Energy and Utilities)
Re: How to find numbers inbetween set  [#permalink]

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04 May 2017, 06:58
1
jwang1191 wrote:
Yeah

The first number divisible by 3 in your set would be -39 and the last would be 99
step 1: subtract largest divisible number in set by the smallest: 99 - (-39) = 138
step 2: divide the difference by the divisible number: 138 / 3 = 46
step 3: add 1: 46 + 1 = 47 total numbers between 99 and -39 that are divisible by 3

This is easy to see with small numbers
For example:
set = from 7 to 21, we need to find number of numbers divisible by 7
21- 7 = 14
14 / 7 = 2
2 + 1 = 3

Yeah its called sequence & series :

Lets say u need to know how many numbers are there between 40 to 100 that are multiple of 3.

So start with first multiple of 3 after 40. In this case it is 42
and the last multiple of 3 before 100. Its 99.
So the formula is

nth term = first term + (n-1)*d
where d is the difference between each of the consecutive numbers. In this case it is 3
n= number of terms (which is what you are looking for)

So using above formula :
nth term is 99
first term is 42
and d is 3

So 99 = 42 + (n-1)*3
57 = (n-1)*3
n-1 = 19
n = 20

You can cross check by any other method ..

This topic is called Sequence and series which we (Indians) study in 11th grade maths...

Hit kudos if this helps!!!
_________________
Re: How to find numbers inbetween set &nbs [#permalink] 04 May 2017, 06:58
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