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

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Senior Manager
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How many integers between 1 and 1000 (inclusive) are divisible by 7  [#permalink]

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Updated on: 21 Oct 2017, 09:54
2
4
00:00

Difficulty:

95% (hard)

Question Stats:

42% (03:29) correct 58% (02:47) wrong based on 53 sessions

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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

Originally posted by RMD007 on 21 Oct 2017, 02:05.
Last edited by RMD007 on 21 Oct 2017, 09:54, edited 2 times in total.
Math Expert
Joined: 02 Aug 2009
Posts: 7106
How many integers between 1 and 1000 (inclusive) are divisible by 7  [#permalink]

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21 Oct 2017, 02:30
1
2
RMD007 wrote:
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

# 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

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..

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Posts: 62
Re: How many integers between 1 and 1000 (inclusive) are divisible by 7  [#permalink]

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21 Oct 2017, 03:29
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

Sent from my Moto G (5) Plus using GMAT Club Forum mobile app
Senior Manager
Status: Countdown Begins...
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Re: How many integers between 1 and 1000 (inclusive) are divisible by 7  [#permalink]

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21 Oct 2017, 22:09

Thanks !!
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Joined: 02 Aug 2009
Posts: 7106
Re: How many integers between 1 and 1000 (inclusive) are divisible by 7  [#permalink]

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21 Oct 2017, 22:17
saicharan1191 wrote:
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

Sent from my Moto G (5) Plus using GMAT Club Forum mobile app

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..
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Re: How many integers between 1 and 1000 (inclusive) are divisible by 7 &nbs [#permalink] 21 Oct 2017, 22:17
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