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# Fraction of numbers from 0 through 1000 that are divisible b

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Founder
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Fraction of numbers from 0 through 1000 that are divisible b [#permalink]  03 May 2019, 02:02
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Question Stats:

80% (00:44) correct 20% (01:31) wrong based on 25 sessions
 Quantity A Quantity B Fraction of numbers from 0 through 1000 that are divisible by both 7 and 10 Fraction of numbers from 0 through 1000 that are divisible by both 5 and 14

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Director
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Re: Fraction of numbers from 0 through 1000 that are divisible b [#permalink]  03 May 2019, 05:22
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For qty A the count of numbers that are divisible by both 7 and 10 are those numbers between 0 and 1000 that are divisible by the LCM of 7 and 10. Since 7 is a prime number the LCM of 7 and 10 is 70. We get the count of numbers as $$\frac{980}{70}$$ = 14. We take 980 because it is the last number less than or equal to 1000 which is divisible by 70. The question does not say that either 0 or 1000 or both are inclusive so in such situation take 1 of the number as inclusive and another exclusive.

For qty B use the same procedure we get the LCM of 5 and 14 as 70 because 5 is a prime number so we simply multiply the two quantities in question. As the LCM for both qty A and B is same and the limit for both the quantity is between 0 and 1000 hence for qty B as well the count of numbers is the same i.e. 14.
Therefore option C

If we had taken 0 and 1000 both inclusive the calculation would be slightly different i.e. $$\frac{980-0}{70}$$ + 1
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Intern
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Re: Fraction of numbers from 0 through 1000 that are divisible b [#permalink]  05 May 2019, 11:19
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In order to be divisible by both 7 and 10, a number has to be divisible by 7, 2, and 5.

In order to be divisible by both 5 and 14, a number has to be divisible by 5, 2, and 7.

Hope this helps.
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Re: Fraction of numbers from 0 through 1000 that are divisible b [#permalink]  08 May 2019, 05:32
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In general, a number that is divisible by two numbers, say a and b, will also be divisible by the LCM of those two numbers. So, since 70 is the LCM in each case there will be an equal number of numbers that are divisible by both 7,10 and 5 and 14. If they had a different LCM the answer would have been different. The answer is C.
Re: Fraction of numbers from 0 through 1000 that are divisible b   [#permalink] 08 May 2019, 05:32
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