Who scores the highest run in a match among five players A, B, C, D, and E?

I. A scores equal to B, who scores five runs more than C.

II. D does not score the highest run, but he scores nine runs more than C.

Choose the correct option based on the sufficiency of the statements:

Question

Who scores the highest run in a match among five players A, B, C, D, and E?

I. A scores equal to B, who scores five runs more than C.

II. D does not score the highest run, but he scores nine runs more than C.

Choose the correct option based on the sufficiency of the statements:

Accepted Answer

**Solution:**

1. From Statement I:
   - A = B
   - B = C + 5
   So, A = B = C + 5
   This tells us A and B score 5 runs more than C.
   However, no information is given about D and E's scores, so we cannot determine who has the highest score.

2. From Statement II:
   - D does not have the highest score.
   - D = C + 9
   This tells us D scores 9 runs more than C but is not the highest scorer.
   No information about A, B, or E is given, so we cannot conclude who scored the highest.

3. Combining Statements I and II:
   - From I: A = B = C + 5
   - From II: D = C + 9 and D is not highest
   Since D scores 9 more than C, and A and B score 5 more than C, D's score is higher than A and B.
   But D is not the highest scorer, so someone else (E) must have scored more than D.
   Therefore, E has the highest score.

Hence, both statements together are necessary to answer the question.

**Answer:** (e) Both Statements I and II together are necessary to answer the question.

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