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what is the number of integers that are not divisible by 7

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what is the number of integers that are not divisible by 7  [#permalink]

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New post 21 Dec 2017, 09:55
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what is the number of integers that are not divisible by 7 in the range of integers from 3 to 500?

A) 70
B) 71
C) 426
D) 427
E) 428

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Re: what is the number of integers that are not divisible by 7  [#permalink]

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New post 21 Dec 2017, 10:18
saswata4s wrote:
what is the number of integers that are not divisible by 7 in the range of integers from 3 to 500?

A) 70
B) 71
C) 426
D) 427
E) 428


Total Number from 3 to 500 \(= 500-3+1=498\)

Numbers that are divisible by 7: first number=7, last number =497, common difference =7

Hence \(497=7+(n-1)*7 => n=71\)

Therefore numbers that are not divisible by 7 \(= 498-71=427\)

Option D
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Re: what is the number of integers that are not divisible by 7  [#permalink]

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New post 22 Dec 2017, 11:23
niks18, can you please explain the concept of what you did?
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what is the number of integers that are not divisible by 7  [#permalink]

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New post 22 Dec 2017, 19:20
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BobsterGMAT wrote:
niks18, can you please explain the concept of what you did?


Hi BobsterGMAT

There is only one concept / formula that needs to be used here. Numbers are in AP series and the formula to find any number in an AP series is

\(T_n=a +(n-1)d\), where \(a\)=first term of the series, \(n\)=number of terms in the series and \(d\)=common difference i.e. difference between any two number in the series,

so here, numbers from 3 to 500 are in AP with \(a=3\), \(d=1\) & \(T_n=500\), we need \(n\)=number of terms. Using the formula, you get-

\(500=3+(n-1)*1 => 500=3+n-1=>n=498\)

Now in this series first number that is divisible by 7 will be 7 itself and the other number will be multiple of 7 so the new series will be 7, 14, 21,28.......\(T_n\) Hence common difference of this series \(d=7\)

to find the last number of this series divide 500 by 7, you will get 3 as remainder which means 3 is extra in 500, so removing 3 will give you a number that will be divisible by 7. ie. 500-3=497 will be divisible by 7 and will be our \(T_n\) for the series

Hence \(T_n=7+(n-1)*7 => n=71\)

Numbers that are not divisible by 7= Total Terms - Terms that are divisible by 7

\(=498-71=427\)
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Re: what is the number of integers that are not divisible by 7  [#permalink]

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New post 29 Jan 2018, 09:59
I am deepening my knowledge about sequences in these days and I found this question simply great! Thanks :-)
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Re: what is the number of integers that are not divisible by 7 &nbs [#permalink] 29 Jan 2018, 09:59
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