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# How many of the positive integers less than 10,000 are divisible by 3

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Math Expert
Joined: 02 Sep 2009
Posts: 61301
How many of the positive integers less than 10,000 are divisible by 3  [#permalink]

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27 Nov 2019, 00:41
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Difficulty:

75% (hard)

Question Stats:

47% (02:14) correct 53% (01:51) wrong based on 43 sessions

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How many of the positive integers less than 10,000 are divisible by 3 or 5?

A. 4,666
B. 4,667
C. 5,132
D. 5,133
E. 5,332

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Joined: 02 Aug 2009
Posts: 8256
Re: How many of the positive integers less than 10,000 are divisible by 3  [#permalink]

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27 Nov 2019, 04:03
Bunuel wrote:
How many of the positive integers less than 10,000 are divisible by 3 or 5?

A. 4,666
B. 4,667
C. 5,132
D. 5,133
E. 5,332

Are You Up For the Challenge: 700 Level Questions

positive integers less than 10,000 that are divisible by 3 = $$\frac{9999}{3}=3333$$
positive integers less than 10,000 that are divisible by 5 = $$\frac{9995}{5}=1999$$

The total 3333+1999, that is 5332, has repetitions in the form of common multiple of 3 and 5..
positive integers less than 10,000 that are divisible by LCM(3,5) or 15 = $$\frac{9990}{15}=666$$

Total = $$5332-666=4666$$

A
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Re: How many of the positive integers less than 10,000 are divisible by 3  [#permalink]

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27 Nov 2019, 09:39
integer <10,000 divisible by 3 ; 10,000/3 ; 3333
integer <10,000 divisible by 5; 1999
LCM ; 15 ; integer <10,000 divisible by 15 ; 666
so total integers less than 10,000 are divisible by 3 or 5 = 3333+1999 - 666 ; 4666
IMO A
Bunuel wrote:
How many of the positive integers less than 10,000 are divisible by 3 or 5?

A. 4,666
B. 4,667
C. 5,132
D. 5,133
E. 5,332

Are You Up For the Challenge: 700 Level Questions
Re: How many of the positive integers less than 10,000 are divisible by 3   [#permalink] 27 Nov 2019, 09:39
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