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How many integers between 1 and 2,000 are divisible by 10, 25, and 35?

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How many integers between 1 and 2,000 are divisible by 10, 25, and 35?  [#permalink]

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New post 19 Apr 2016, 03:09
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A
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C
D
E

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Re: How many integers between 1 and 2,000 are divisible by 10, 25, and 35?  [#permalink]

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New post 19 Apr 2016, 04:15
Prime factorization of given numbers
10=2*5
25=5^2
35=5*7
LCM of the given numbers
=2*5^2*7
=50*7
=350

Therefore , number of integers = 2000/350
=5

Answer C
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Re: How many integers between 1 and 2,000 are divisible by 10, 25, and 35?  [#permalink]

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New post 19 Apr 2016, 10:54
1
I find it easiest to just take 350 and see how many times it fits in 2000. Which is five times. Anything lower than 350 is impossible as anything divisible by 35 won't be divisible by 10 and 25.

Answer is 5.
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Re: How many integers between 1 and 2,000 are divisible by 10, 25, and 35?  [#permalink]

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New post 19 Apr 2016, 11:14
Bunuel wrote:
How many integers between 1 and 2,000 are divisible by 10, 25, and 35?

A. 4
B. 5
C. 6
D. 7
E. 8


Since the numbers are divisible by 10, 25, and 35 they must be the common multiples of these 3 Numbers (10, 25, and 35)

LCM of 10, 25, and 35 is 350

Numbers divisible by 350 is 2000/350 = 5.xxxxx

So, There must be 5 integers between 1 and 2,000 are divisible by 10, 25, and 35. :-D :lol: :P
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Re: How many integers between 1 and 2,000 are divisible by 10, 25, and 35?  [#permalink]

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New post 19 Apr 2016, 14:39
The question basically asks us to calculate the LCM of 10, 25 and 35 and use that number to find how many numbers are divisible by it within the given range.

LCM of 10, 25 and 35 = 350

Numbers divisible by 350 from 1 to 2000 : 350, 700, 1050, 1400, 1750
Only 5 numbers
Correct Option : B
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Re: How many integers between 1 and 2,000 are divisible by 10, 25, and 35?  [#permalink]

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Re: How many integers between 1 and 2,000 are divisible by 10, 25, and 35?  [#permalink]

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Re: How many integers between 1 and 2,000 are divisible by 10, 25, and 35?   [#permalink] 16 Aug 2018, 18:35
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