A, B, C, D, E, F and G each scored a different marks in an exam and all marks were integers. Only three people scored more than F. Only G scored less than B. More than three people scored between G and D. C scored less than E and no one scored between C and E. If E scored 90, F scored 84 and the second lowest score was 71, which of the following may be the possible score of A?
A, B, C, D, E, F and G each scored a different marks in an exam and all marks were integers. Only three people scored more than F. Only G scored less than B. More than three people scored between G and D. C scored less than E and no one scored between C and E. If E scored 90, F scored 84 and the second lowest score was 71, which of the following may be the possible score of A?
Solution
Looking at the given information, let me establish the ranking from highest to lowest score.
Finding the positions:
Since only three people scored more than F (84), F is at the 4th position.
Since only G scored less than B, and the second lowest score was 71:
- B scored 71 (6th position)
- G is at 7th position (lowest)
Finding D's position:
"More than three people scored between G and D" means at least 4 people are between them.
G is at position 7. If 4 people are between G and D → D is at position 2
If 5 people are between G and D → D is at position 1
So D must be in the top 2 positions.
Finding E and C's positions:
E scored 90, which is greater than F's 84, so E is in the top 3.
"C scored less than E and no one scored between C and E" means C and E are consecutive in ranking.
Since E is in top 3 and C is just below E:
- If E is 2nd, C is 3rd → D must be 1st ✓
- If E is 3rd, C would be 4th, but F is already 4th ✗
Therefore: D is 1st, E is 2nd, C is 3rd
Complete ranking:
| Position | Person | Score |
|---|---|---|
| 1st | D | ? |
| 2nd | E | 90 |
| 3rd | C | ? |
| 4th | F | 84 |
| 5th | A | ? |
| 6th | B | 71 |
| 7th | G | ? |
A is at 5th position, between F (84) and B (71).
So A's score must satisfy: 71 < A < 84
Checking the options:
- 95: Too high ✗
- 88: Too high ✗
- 79: Fits perfectly (71 < 79 < 84) ✓
- 63: Too low ✗
The answer is 79.