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      Question

      Average of A, B and C is 30 and

      that of C, D and E is 19. The average of A and E is 23 and that of B and E is 24. Find the value of B.
      A 20 Correct Answer Incorrect Answer
      B 18 Correct Answer Incorrect Answer
      C 25 Correct Answer Incorrect Answer
      D Can't be determined Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

      From the equations derived: A+B+C=90 C+D+E=57 A+E=46 B+E=48 We expressed everything in terms of A: E=46−A B=2+A C=88−2A D=3A−77 However, no unique value of A is determined from these equations because the system of equations is under determined. There are more variables (A,B,C,D,E) than independent equations. This means multiple sets of values can satisfy the equations, making it impossible to uniquely determine B. Thus, the answer is indeed "cannot be determined."

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