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How many integers between 1 and 1000 (inclusive) are divisible by 7

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RMD007
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How many integers between 1 and 1000 (inclusive) are divisible by 7 [#permalink] How many integers between 1 and 1000 (inclusive) are divisible by 7   Updated on: 21 Oct 2017, 10:54
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How many integers between 1 and 1000 (inclusive) are divisible by 7 or 3 but not by 5?

A. 391

B. 343

C. 438

D. 466

E. 475


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B

Originally posted by RMD007 on 21 Oct 2017, 03:05.
Last edited by RMD007 on 21 Oct 2017, 10:54, edited 2 times in total.
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chetan2u
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How many integers between 1 and 1000 (inclusive) are divisible by 7 [#permalink] How many integers between 1 and 1000 (inclusive) are divisible by 7   21 Oct 2017, 03:30
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RMD007
How many integers between 1 and 1000 (inclusive) are divisible by 7 or 3 but not by 5?

A. 391

B. 419

C. 438

D. 466

E. 475


Source: Self - made


# div by 7 = 1000/7 = 142.8 = 142
# div by 3 = 1000/3 = 333.3 = 333
# div by both 7 and 3 = 1000/21 = 47
# div by both 7 and 5 = 1000/35 = 28
# div by 5 and 3 = 1000/15 = 66
# div by 3,5,7 = 1000/105 = 9

so for our answer
we add div by 7 and div by 3, thereafter subtract those div by both 7 and 3 as they have been added twice in the process..
Now they cannot contain div by 5, so we subtract div by both 7 and 5 and thereafter div by both 3 and 5..
But in the process some numbers are eliminated twice so we add multiple of all three -3,5, and 7.
ans 142+333-47-28-66+9=343..

pl relook into your answers
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saicharan1191
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Re: How many integers between 1 and 1000 (inclusive) are divisible by 7 [#permalink] How many integers between 1 and 1000 (inclusive) are divisible by 7   21 Oct 2017, 04:29
I am getting 390 as the answer.
333+142- (9+57+19) =390
333 = multiples of 3
142 = multiples of 7
9= multiples of 3,7,5
57 = multiples of 3,5 but not 7
19 = multiples of 5,7 but not 3

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Re: How many integers between 1 and 1000 (inclusive) are divisible by 7 [#permalink] How many integers between 1 and 1000 (inclusive) are divisible by 7   21 Oct 2017, 23:09
Added correct answer choice! :)

Thanks !!
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Re: How many integers between 1 and 1000 (inclusive) are divisible by 7 [#permalink] How many integers between 1 and 1000 (inclusive) are divisible by 7   21 Oct 2017, 23:17
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saicharan1191
I am getting 390 as the answer.
333+142- (9+57+19) =390
333 = multiples of 3
142 = multiples of 7
9= multiples of 3,7,5
57 = multiples of 3,5 but not 7
19 = multiples of 5,7 but not 3

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hi..

when you ADD div by 3 and div by 7, it duplicates few numbers - COMMON multiple of 3 and 7 and these require to be SUBTRACTED from total, which you have missed out..
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Re: How many integers between 1 and 1000 (inclusive) are divisible by 7 [#permalink] How many integers between 1 and 1000 (inclusive) are divisible by 7   10 Aug 2024, 11:10
Ans=
142-38-9-19
+
333-38-57-9
+
38

=343­
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Re: How many integers between 1 and 1000 (inclusive) are divisible by 7 [#permalink]
10 Aug 2024, 11:10
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