**Direction for the questions: (1- 3:)** **Study following information to answer the given questions:**

Each of the six friends A,B,C,D,E and F. All of them appeared for the same exam but scored different marks. E did not score the lowest number of marks. C scored more than only A and E. D scored less than only B. The third highest score was 91 marks. E scored 76 marks. The highest score was 20 marks more than the score of E. The lowest score is half the highest score.

**Additional information for the question 3 : **There was a mistake is writing down the marks of the person with the lowest score. The digits were marked in the reverse order, and his score was corrected by placing the two digits in the correct order.

**Question 1:** Who has the lowest score?

(a) A

(b) C

(c) D

(d) F

**Question 2:** Which could be C’s score?

(a) 92

(b) 74

(c) 78

(d) 70

**Question 3:** The highest ranking that A can possibly secure is:

(a) second-last

(b) third-last

(c) fourth-highest

(d) cannot be determined

### Answers and Explanations

**Explanation for questions 1 to 3:**

From the conditions given above, we can obtain the order of marks obtained by the six friends as: B>D>F>C>E>A

From this we know that F scored 91 marks and E scored 76 marks.

Also, the highest score is 96, scored by B.

Lowest score is of A, and it is 48.

**Answer 1 : (a)**

We can see from the above that A has the lowest score.

**Answer 2 : (c)**

The score of C has to be between the score of F and E. Therefore, the one figure possible is 78.

**Answer 3 : (c)**

The question does not ask us to determine the exact rank, it only asks about a possible rank. In the given case, the correct marks for A would be 84. This would place him over E for sure, but we are not sure whether he is placed over C or not. This means that the highest ranking he can take is fourth-highest, as his marks are still less that F (91).

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