Micro economics question

[harish]

Can someone explain how the answer is derived ?

 Professor Goodheart's colleague Dr. Kremepu gives 3 midterm exams. He drops the lowest and gives each student her average score on the other two exams. Polly Sigh is taking his course and has a 60 on her rst exam. Let x2 be her score on the second exam and x3 be her score on the third exam. If we draw her indierence curves for scores on the second and third exams with x2 represented by the horizontal axis and x3 represented by the vertical axis, then her indierence curve through the point (x2;x3) = (50;70) is:

(a) L-shaped with a kink where x2 = x3.
(b) three line segments, one vertical, one horizontal, and one running from (70;60) to (60;70).
(c) a straight line, running from (0;120) to (120;0).
(d) three line segments, one vertical, one horizontal, and one running from (70;50) to (50;70).
(e) a V-shaped curve with its point at (50;70).

The correct answer is b apparently.

[Abhitesh]

Given,
Score in Ist exam = 60.
IC passes through (50,70). So average a = 65.
Think about following.
Can both x2 and x3 be less than 60? Both more than 60?
What happens if only x2>=60? What if only x3>=60?

[Amit Goyal]

Let x be the score in exam 2 and y be the score in exam 3. So,
u(x, y)  = (x+y)/2 when 60 <= min(x, y),
u(x, y)  = (max(x, y) + 60)/2 when  min(x, y) < 60

Now try and plot indifference curve for u = 65.