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26 May 2017, 04:43
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If the median of the 5 integers is 10, is the range of the integers greater than 4?
(1) The average (arithmetic mean) of the 5 integers is 12.
(2) The smallest of the 5 integers is 10.
(1) The average (arithmetic mean) of the 5 integers is 12.
(2) The smallest of the 5 integers is 10.
26 May 2017, 04:43
Kudos
Bookmarks
Official Solution:
First, if the question is about "greater than" you should get the least value. In other words, every other number is "greater than" the least value of the range.
In the original condition, there are 5 variables (5 integers) and 1 equation (median=10). In order to match the number of variables to the number of equations, there must be 4 equations. Therefore, E is most likely to be the answer. By solving con 1) and con 2),
In order to get the least value of the range, the smallest of 5 integers should be the maximum value, and the largest should be the minimum. Also, since the total average is 12, the total sum should be \(12 * 5 = 60\).
Thus, there must be 10, 10, 10, 15, and 15, in order for the range to become the minimum value as shown below.
10, 10, 10, 15, 15
At this time, \(range = 15 - 10 = 5 > 4\), hence yes, it is sufficient. The answer is C.
However, this question, too, is an integer and statistics question, one of the key questions, so you should apply "CMT 4(A: if you get C too easily, consider A or B)".
In the case of con 1), the average of 5 integers is 12, so the sum is 60 and it should be the minimum value of the range. The smallest of 5 integers becomes the maximum value and the largest should be the minimum value. So, the case where the range becomes the minimum value is when you get 10, 10, 10, 15, 15. At this time, \(range = 15 - 10 = 5 > 4\), hence yes, it is sufficient.
In the case of con 2), from 10, 10, 10, 15, 15, \(range = 15 - 10 = 5 >4\), hence yes, but from 10, 10, 10, 11, 11, \(range = 11 - 10 = 1 < 4\), hence no, and therefore, it is not sufficient. The answer is A.
Answer: A
First, if the question is about "greater than" you should get the least value. In other words, every other number is "greater than" the least value of the range.
In the original condition, there are 5 variables (5 integers) and 1 equation (median=10). In order to match the number of variables to the number of equations, there must be 4 equations. Therefore, E is most likely to be the answer. By solving con 1) and con 2),
In order to get the least value of the range, the smallest of 5 integers should be the maximum value, and the largest should be the minimum. Also, since the total average is 12, the total sum should be \(12 * 5 = 60\).
Thus, there must be 10, 10, 10, 15, and 15, in order for the range to become the minimum value as shown below.
10, 10, 10, 15, 15
At this time, \(range = 15 - 10 = 5 > 4\), hence yes, it is sufficient. The answer is C.
However, this question, too, is an integer and statistics question, one of the key questions, so you should apply "CMT 4(A: if you get C too easily, consider A or B)".
In the case of con 1), the average of 5 integers is 12, so the sum is 60 and it should be the minimum value of the range. The smallest of 5 integers becomes the maximum value and the largest should be the minimum value. So, the case where the range becomes the minimum value is when you get 10, 10, 10, 15, 15. At this time, \(range = 15 - 10 = 5 > 4\), hence yes, it is sufficient.
In the case of con 2), from 10, 10, 10, 15, 15, \(range = 15 - 10 = 5 >4\), hence yes, but from 10, 10, 10, 11, 11, \(range = 11 - 10 = 1 < 4\), hence no, and therefore, it is not sufficient. The answer is A.
Answer: A
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