text: # Difficult Pie Charts Solved QuestionData Interpretation Discussion
  
  Common Information
  
  Answer the questions on the basis of the information given below.
  
  The following Pie-Chart provides information about the marks obtained by six students A, B, C, D, E and F in four different subjects P, Q, R and S. The marks obtained by each of the students in subject P is indexed to the maximum marks that can be obtained in subject P. This holds true for the other three subjects as well.
  
  For example, if the maximum marks that can be obtained in subject P is ‘40k’, then the marks obtained in subject P by student A is 15k, by student B is 20k and so on. This holds true for the marks obtained by the students in the other three subjects as well.
  
  The marks obtained by A in subject P is not less than that obtained by him in subject Q or subject R, but not more than that obtained by him in subject S. This holds true for the marks obtained by each of the other 5 students as well.
  
   Q. Common Information Question: 2/5 A student is said to have passed a given subject, if and only if he has obtained at-least 40% of the maximum marks that can be obtained in that subject. In how many of the subjects at least three of the students have passed?
   ✖ A. 0 ✔ B. 1 ✖ C. 2 ✖ D. 3
  
  Solution:
  Option(B) is correct
  
  Let the maximum marks which can be obtained in the subjects P, Q, R and S be $40p, 50q, 60r$ and $80s$ respectively.
  
  From the given information we can conclude that:
  
  $15p≥20q$, $20p≥10q$, $25p≥15q$, $10p ≥18q$, $25p≥32q$ and $30p≥ 12q$
  
  $⇒ p ≥ 1.8q$ -------- (i)
  
  $15p≥8r$, $20p≥16r$, $25p≥20r$, $10p≥24r$, $25p≥10r$ and $30p≥20r$
  
  $⇒ p≥2.4r$ -------- (ii)
  
  $15p≤25s$, $20p≤15s$, $25p≤20s$, $10p≤30s$, $25p≤10s$ and $30p≤35s$
  
  $⇒ p≤ 0.4s$ -------- (iii)
  
  In subject P, the students who have obtained not less than 40% of the maximum marks that can be obtained are B, C, E and F.
  
  There is no other subject in which there are at-least 3 students who have passed.
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