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20 Jan 2022, 08:15
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C
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150, 200, 250, n
Which of the following could be the median of the 4 integers listed above?
I. 175
II. 215
III. 235
A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
Which of the following could be the median of the 4 integers listed above?
I. 175
II. 215
III. 235
A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
20 Jan 2022, 08:25
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Bunuel
Extrapolate from the Info:
Note that we have 4 elements in the list, which is an even number of elements. Then the median of this list will effectively be an average of the two middle numbers.
With an n < 150, our median would be the average of 150 and 200, which is 175.
With n > 250, the median would be the average of 200 and 250, which is 225.
Then we can conclude the median must be between 175 and 225, inclusive. Thus option I is viable with n < 150, and option II would be possible if we let n = 230.
Option III is out of range, so we can only select I and II.
Answer: C
10 Jun 2023, 19:44
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lg800
In order to find the median, we need to arrange the numbers in ascending order. Here in this question, n can be the smallest, largest, or in between 150 & 200 or 200 & 250. So four positions are possible.
N, 150, 200, 250
150, N, 200, 250
150, 200, N, 250
150, 200, 250, N
Median of even number of terms = average of the two middle terms. In this case, average of 2nd and 3rd terms.
If N is smallest, median is 175, and if N is largest, median is 225. So, median will be between 175 to 225 (both inclusive).
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