jack0997 wrote:15, 20, 25, x: (not in order)
Which of the following could be the median of the four integers listed above?
I. 17.5
II. 21.5
III. 23.5
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) All of them
Strategy:
List the four values in ascending order, while testing different positions for x.
Case 1: x, 15, 20, 25
Here, median = (15+20)/2 = 17.5
Thus, Option I (17.5) is a possible median.
Eliminate B and D, which do not include Option I.
Options II and III each indicate a median greater than 20.
A median greater than 20 is possible only if the two smallest numbers are 15 and 20.
Case 2: 15, 20, x, 25
Here, the least possible value for x is 20, while the greatest possible value for x is 25.
If x=20, median = (20+20)/2 = 20.
If x=25, median = (20+25)/2 = 22.5
Implication:
In Case 2, the median can be any value between 20 and 22.5, inclusive.
Thus, Option II (21.5) is a possible median.
Eliminate A, which does not include Option II.
Case 3: 15, 20, 25, x
Median = (20+25)/2 = 22.5.
Implication:
The greatest possible median is 22.5.
Thus, Option III (23.5) is not a possible median.
Eliminate E, which includes Option III.
The correct answer is
C.
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