Seven people A, B, C, D, E, F and G scored different marks (out of 100) in an exam. G scored the lowest marks. B scored second highest marks, which were 80. A scored 72. E scored more than F but less than C. Marks scored by C were a multiple of 11 and less than 70. The sum of marks scored by C and F was 120. What is the score of F?

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**Solution:** 1. Given that B scored the second highest marks, which are 80, and A scored 72. 2. G scored the lowest marks. 3. C's marks are a multiple of 11 and less than 70. Possible multiples of 11 less than 70 are: 11, 22, 33, 44, 55, 66. 4. The sum of marks scored by C and F is 120, so: $$C + F = 120$$ 5. Since E scored more than F but less than C, the order for these three is: $$C > E > F$$ 6. Test possible values for C: - If $C = 66$, then $F = 120 - 66 = 54$ - Check if E can be between 54 and 66 (i.e., $54 < E < 66$), which is possible. 7. Other values for C (like 55, 44, etc.) would give F as 65, 76, etc., which do not fit the conditions (F must be less than E and less than C, and all scores are distinct). 8. Therefore, the correct scores are: - $C = 66$ - $F = 54$ **Answer:** 54

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