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by GMATGuruNY » Mon Jul 28, 2014 4:56 am
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
Let m = the median.

Case 1: 150, 200, 250, n
This case will yield the greatest possible median.
Here, m = (200+250)/2 = 225.
Since it's not possible that m=235, eliminate any answer choice that includes statement III.
Eliminate D and E.

Case 2: 150, 200, n, 250.
Here, n must be between 200 and 250, inclusive.
Least possible median:
If n=200, m = (200+200)/2 = 200.
Greatest possible median:
If n=250, m = (200+250)/2 = 225.
Thus:
200 ≤ m ≤ 225.
Since it's possible that m=215, eliminate any remaining answer choice that does not include statement II.
Eliminate A.

Case 3: 150, n, 200, 250
Here, n must be between 150 and 200, inclusive.
Least possible median:
If n=150, m = (150+200)/2 = 175.
Since it's possible that m=175, eliminate any remaining answer choice that does not include statement I.
Eliminate B.

The correct answer is C.
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by Brent@GMATPrepNow » Mon Jul 28, 2014 7:04 am
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
In cases where there is an EVEN number of values (as there are in this question), the median will be the average of the two middlemost values when all values are arranged in ascending order.

We can already see that 200 will be one of the two middlemost values, so let's check the various options for median and see what the other number needs to be to get each target median.

I. 175
If the median is 175, then it must be the case that (200 + other number)/2 = 175
So, in this case, the other number must be 150.
This is entirely possible, if n < 150. For example if n = 100, then the values would be {100, 150, 200, 250}, in which case the median is 175.
So, option I is possible.

II. 215
If the median is 215, then it must be the case that (200 + other number)/2 = 215
So, in this case, the other number must be 230.
This is entirely possible, if n = 230. The values would be {150, 200, 230, 250}, in which case the median is 215.
So, option II is possible.

III. 235
If the median is 235, then it must be the case that (200 + other number)/2 = 235
So, in this case, the other number must be 270.
Here, we have a PROBLEM. If the other number is 270, then the values are {150, 200, 250, 270}, in which case 200 and 270 are NOT the two middlemost values. The two middlemost values are 200 and 250, giving us a median of 225 (not 235).
So, option III is NOT possible.

Answer: C

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by GMATinsight » Mon Jul 28, 2014 8:03 am
CONCEPT :
If Number of terms in set is ODD: Median is the Middle term when the terms are arranged in Ascending/Descending order
If Number of terms in set is EVEN: Median is the AVERAGE OF TWO Middle term when the terms are arranged in Ascending/Descending order

Terms in Set are : 150, 200, 250, n

Since the value of n is unknown therefore there are three cases

Case 1: n is the Biggest term of the set
Median = (200+250)/2 = 225

Case 2: n is the Smallest term of the set
Median = (150+200)/2 = 175

Case 3: n is the Greater than 150 and lesser than 250
then, 175 < Median < 225

Therefore,
Answer : Option C
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by peterparker » Sat Aug 02, 2014 10:51 pm
Median, middle element if the numbers are odd, else, for even set, the average of the two middle element.

Now, here, 150,200,250,n set are given, and we have to determine the median.

when median = 175, then, median = (200 + n)/2, which means, that n = 150, which is possible.

When median = 215, n = (430 - 200) = 230, a combination which is possible.

When median = 235, then n = 470 - 200 = 270 > 250, this option strikes out, because, median of 200 + 250 is 225,

So the correct answer is the option which has I and II
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