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Fraction of numbers from 0 through 1000 that are divisible b
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03 May 2019, 02:02
03 May 2019, 02:02
Expert Reply
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Question Stats:
78% (00:47) correct
21% (01:37) wrong based on 61 sessions
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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.
Re: Fraction of numbers from 0 through 1000 that are divisible b
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05 May 2019, 11:19
05 May 2019, 11:19
5
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.
Answer: C.
Hope this helps.
In order to be divisible by both 5 and 14, a number has to be divisible by 5, 2, and 7.
Answer: C.
Hope this helps.
General Discussion
Re: Fraction of numbers from 0 through 1000 that are divisible b
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03 May 2019, 05:22
03 May 2019, 05:22
1
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
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
