15, 20, 25, x: (not in order)

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

OA C

We know that the median is the middle-most value of any series/dataset, but we do not know
the value of x, so we cannot calculate the exact value of Median; however, we can surely find its
range.

Case 1: If x is smallest, the series would be x; 15; 20; 25 and median = average of 15 & 20 =
17.5–smallest median value.

Case 2: If x is largest, the series would be 15; 20; 25; x and median = average of 20 & 25 =
22.5–largest median value.

Thus, the median would lie between 17.5 & 22.5, inclusive. Since only options, I & II are in the
range, option C is correct.

The correct answer: C

Hope this helps!

-Jay

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Hi jack0997,

This is a great 'concept' question, meaning that if you recognize the concepts involved, then you don't have to necessarily work through as much 'math.'

We're given 4 numbers (3 integers and one variable) and asked to determine what the median of the group COULD be... Since the median of a group with an EVEN number of terms is the AVERAGE of the two 'middle terms', we have to think about what the X could be (in relation to the other numbers in the group).

If we made the X small (X=0, for example), then the group would be:
(0, 15, 20, 25)
The median would be (15+20)/2 = 35/2 = 17.5
Roman Numeral 1 IS a possible median.

If we made the X a specific "middle value" (X=23), then the group would be:
(15, 20, 23, 25)
The median would be (20+23)/2 = 43/2 = 21.5
Roman Numeral 2 IS a possible median.

If we made the X big (X=100, for example), then the group would be:
(15, 20, 25, 100)
The median would be (20+25)/2 = 45/2 = 22.5... but the median could NEVER be bigger than 22.5
Roman Numeral 3 is NOT a possible median.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

jack0997 wrote: ↑

Thu Jul 13, 2017 5:16 am

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

OA C

If x ≤ 15, then the data values are x, 15, 20, 25, and the median is (15 + 20)/2 = 35/2 = 17.5. We see that I could be true.

If x is between 15 and 25 (i.e., 15 < x < 25), then the median is (20 + x)/2, which is some value between between 17.5 and 22.5. We see that II could also be true.

No matter what the value of x (when x is the largest data value), the median can never exceed (20 + 25)/2 = 22.5. Thus, Statement III can never be true.

Answer: C