Median

[nehakhas1]

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
Ans : C
Please explain

[sairakesh]

Given Numbers are 150,200,250 and n.
Here Median is avg of 2nd number and 3rd number where 4 th number n is gretaer than 250.
so (200+250) /2 =225.

Now lets consider the value of n be lessthan 250(consider 230)
so now the numbers will be 150,200,230,250.
so median is (200+230)/2 = 215.


Now lets consider the value of n be lessthan 150(consider 130)
so now the numbers will be 130,150,200,250.
so median is (150+200)/2 = 175.

so the possible median values will be from 175 to 225.

So answer C is correct

[sureshbala]

This can be answered fast if you consider the options given rather than all the possibilities of n.

Since we have 4 numbers, the median is the average of the two numbers when these 4 numbers are written in ascending(descending) order.

Give first value is 175.

So the sum of the two numbers must be 350. This possible if n < 150

Second value is 215.

So the sum of the two numbers must be 430. This is possible if n = 230.

Third value is 235.

So the sum of the two numbers must be 470. This is not possible for any given value of n.

Hence I and II are possible but not III