If n<=150
Then middle two numbers are 150 and 200, hence median is 175

If n>=250
Then middle two numbers are 200 and 250, hence median is 225

These define the max and min median possible. If n is between 150 and 250, the median will be between 175 and 225

In conclusion, median has to be between 175 & 225
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1) 175. This is possible if N < 150 Implies that the two middle numbers are 150 and 200.
2) 215. This is possible if 200 < N < 250 and if (N+200)/2 = 215. i.e. N=230.
3) 235. This is not possible because again, this would require 200 < N < 250. And since 235 is closer to 250 we would require 250-235 = 235-N. N=210. However, now 235 is no longer the median of the set.

Hence C.

I. If n = 150, then the median is 175, so I works
II. If n = 230, then the median is 215, so II works
III. You cannot pick a value for n that makes the median 235

Answer is C

I if n is <= 150 median is 175
II if n = 230 then median is 215
III no possible values of n because for median to be 235 n has to be greater than 250 and if n is >250 then n cannot be used to determine median

Hope it help
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Median is the middle number if set of numbers are odd
or the mean of middle 2 numbers if set of numbers are even
Example - set of 1,2,3,4,5 (median is 3)
se of 1,2,3,4,5,6 (median is 3.5)

In our question here, we have a set of 4 numbers 150,200,250,n
so median is the mean of 2 middle numbers.

III option is if the median could be 235.
For a average 235 atleast one number should be greater than 235
If n is less than 250 and greater than 235, average of 2 mumbers (200 and any number between 235 and 250) can never be 235.
If the n is greater than 250 then median is average of 200 and 250 i.e. 225
Hence 235 can never be the median

Hope this help!!!!!
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Q1 - Answer c

As we know there are 4 numbers in the list

So the Median will be half of the sum of the two numbers

So now lets look at the options.

175 cane be the median if n is less than 150 ( (150 + 200)/2 = 175)
215 can also be the median if n is 230
235 cant be because if the median is 235 then that means ( n+ 200) / 2= 235 => n = 270 and in case n is 270 then the median should be 200 + 250 / 2 = 225

Q 2, I am not able to understand the this Q as its not properly written, could you please write this question again so that we can try to answer that one as well.

Answer is C

n< 150 -> median = 350 / 2 = 175

250>n>200 median let n = 230 median = 215

n > 250 median = (200+250)/2 = 225
median can not be greater than 225. therefore III is wrong.

I & II are correct.

[quote="soumanag"]Answer is C

n< 150 -> median = 350 / 2 = 175

250>n>200 median let n = 230 median = 215

n > 250 median = (200+250)/2 = 225
median can not be greater than 225. therefore III is wrong.

I & II are correct.[/quote


Didn't understand still!!!

Make following ordered sequence

n, 150, 200, 250
150,n,200, 250
150, 200, n, 250
and 150,200,250, n

After that same explaination as above

Since there are four numbers in the set, the median will be the average of the two middle numbers. There are three possibilities for n we need to consider.

If n < 150, then the median is (150 + 200) / 2 = 175.
If n > 250, then the median is (200 + 250) / 2 = 225.
If 150 < n < 250, the median will be (200 + n) / 2, or 100 + (n/2). So the median will range between 175 and 225.

III is the only answer which does not fall in this range, so the answer is I and II - (C).

n could be placed in following positions:

1. 150, 200, 250, n
2. 150, 200, n, 250
3. 150, n, 200, 250
4. n, 150, 200, 250

Case 1

Whether n is 250 or any number more than 250, the median will always be average of 2 middle nos. (200 and 250). Median would be 225. Not one of the given options

Let us take case 4 first
Case 4

Whether n is 150 or any number less than 150, the median will always be average of 2 middle nos. (150 and 200). Median would be 175, option (1) is certainly true.

Case 2

n can be 200 or 250 or any value between 200 and 250.
If n is 200, median = 100 --> not one of given options.
If n is 250, median would be 225. Not one of the given options.

If 200<n<250, then let us check whether the median [(200+n) / 2] is equal to given options (215 & 235)

200+n = [215 *2 = 430]. Which means n = 230. This is acceptable value. Option (2) is also true.
200+n = [235 * 2 = 470]. Which means n = 270. But This value is not between 200 and 250.
We get one acceptable and one non-acceptable value.
Option 3 is Not acceptable.


Case 3

n can be 150 or 200 or any value between 150 and 200.
If n is 150, median = 175 --> option already considered .
If n is 200, Median would be 200. Not one of the given options.

If 150<n<200, then let us check whether the median [(200+n) / 2] is equal to given options (215 & 235)
we will get n=230 and 270. Both not acceptable for this case.

So (1) and (2) are correct. Option (C) is the correct answer.

235 cannot be the median
For set with even # of elements ; Median= \(\frac{Sum of Middle 2 terms}{2}\)
\(\frac{Sum of middle 2 terms}{2}=235\) (if we want 235 to be the median)

Sum of middle two terms = 235*2
Sum of middle two terms = 470

If we take n to be largest term then 200 and 250 will become the middle term (150,200,250,any term larger than 250)
200+ 250=450 it is not 470


If we take 250 to be the largest term then n will become a smaller term such as 249 (150,200,249,250)

then 200+249= 449

we cannot get 470 in any possible way
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