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26 May 2017, 04:43
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There are 5 integers such that the difference of the biggest number and the median is 3. Is the average (arithmetic mean) of the integers smaller than the median?
(1) The median of the 5 integers is 16.
(2) The difference of the median and the smallest number is 8.
(1) The median of the 5 integers is 16.
(2) The difference of the median and the smallest number is 8.
26 May 2017, 04:43
Kudos
Bookmarks
Official Solution:
If you look at the original condition, there are 5 variables (5 integers) and 1 equation (B-M=3: B: biggest and M: median). In order to match the number of variables to the number of equations, there must be 4 more questions. Therefore, E is most likely to be the answer.
Also, if the question is about "smaller than" you should get the maximum value. In other words, you have to get the maximum value of the average, because if the maximum value of the average is smaller than the median, then everything is small. By solving con 1) & con 2),
the maximum value of the average is \(\frac{8+16+16+19+19}{5}=15.6 16\) no, hence it is not sufficient.
In the case of con 2), the maximum value of the \(average = \frac{(M-8)+M+M+(M+3)+(M+3)}{5} = \frac{5M-2}{5} < M\), hence yes, it is sufficient. The answer is B.
Answer: B
If you look at the original condition, there are 5 variables (5 integers) and 1 equation (B-M=3: B: biggest and M: median). In order to match the number of variables to the number of equations, there must be 4 more questions. Therefore, E is most likely to be the answer.
Also, if the question is about "smaller than" you should get the maximum value. In other words, you have to get the maximum value of the average, because if the maximum value of the average is smaller than the median, then everything is small. By solving con 1) & con 2),
the maximum value of the average is \(\frac{8+16+16+19+19}{5}=15.6 16\) no, hence it is not sufficient.
In the case of con 2), the maximum value of the \(average = \frac{(M-8)+M+M+(M+3)+(M+3)}{5} = \frac{5M-2}{5} < M\), hence yes, it is sufficient. The answer is B.
Answer: B
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