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

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Current Student
Joined: 27 May 2014
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what is the number of integers that are not divisible by 7  [#permalink]

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21 Dec 2017, 09:55
1
00:00

Difficulty:

45% (medium)

Question Stats:

63% (01:34) correct 37% (01:22) wrong based on 83 sessions

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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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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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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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22 Dec 2017, 19:20
1
1
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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29 Jan 2018, 09:59
I am deepening my knowledge about sequences in these days and I found this question simply great! Thanks
Re: what is the number of integers that are not divisible by 7 &nbs [#permalink] 29 Jan 2018, 09:59
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