Read the following information carefully and answer the question that follows.
Nine students scored different marks in a test. G's score is immediately lower than E's score. Three students scored marks between G and D. I's score is immediately higher than B's score and immediately lower than D's score. Five students scored marks between E and I. H scored a higher score than E. A scored higher than C but lower than G. F scored lower than C but higher than D.
Who among the following scored the third lowest marks in the test?
Correct Answer :
D
Solution :
To determine who scored the third lowest marks in the test, let us arrange all nine students in descending order of their scores from position 1 (highest) to position 9 (lowest).
Step 1: Analyze the given conditions step-by-step.
1. G's score is immediately lower than E's score: This means E and G are placed together as (E, G).
2. I's score is immediately higher than B's score and immediately lower than D's score: This means D, I, and B are placed together as (D, I, B).
3. Five students scored marks between E and I: Since E is above G, E must be above I. With 5 students between E and I, the positions of E and I will have a difference of 6 (i.e., Position of I = Position of E + 6).
Step 2: Determine the positions of E, G, D, I, and B.
If E is at position 1:
- G is at position 2.
- Since 5 students are between E (1) and I, I must be at position 7.
- Since (D, I, B) are consecutive, D must be at position 6 and B must be at position 8.
Now, let us check the condition: "Three students scored marks between G and D".
- Position of G = 2
- Position of D = 6
- Students between G and D are at positions 3, 4, and 5, which is exactly 3 students. This perfectly matches the condition!
So far, our arrangement from 1 to 9 is:
1. E
2. G
3. _
4. _
5. _
6. D
7. I
8. B
9. _
Step 3: Place the remaining students (H, A, C, F).
4. H scored a higher score than E: Since E is at position 1, wait, H must be higher than E. This means E cannot be at position 1 unless H is at position 1 and E shifts down. Let's re-verify the positions with H higher than E.
Let's shift the positions down by 1:
1. H
2. E
3. G
4. _
5. _
6. _
7. D
8. I
9. B
Let's re-verify all conditions for this arrangement:
- H is higher than E: Position 1 (H) > Position 2 (E) - Valid.
- G is immediately lower than E: Position 2 (E), Position 3 (G) - Valid.
- Five students between E and I: E is at 2, I is at 8. Positions between them are 3, 4, 5, 6, 7 (5 students) - Valid.
- I is immediately higher than B and immediately lower than D: D is at 7, I is at 8, B is at 9 - Valid.
- Three students between G and D: G is at 3, D is at 7. Positions between them are 4, 5, 6 (3 students) - Valid.
Now let's place the remaining students: A, C, F into positions 4, 5, 6.
- "A scored higher than C but lower than G": So A > C, and A is lower than G (position 3).
- "F scored lower than C but higher than D": So C > F, and F is higher than D (position 7).
- Combining these: G > A > C > F > D.
- Therefore, the positions 4, 5, and 6 must be filled by A, C, and F respectively:
Position 4: A
Position 5: C
Position 6: F
Step 4: Final complete ranking from highest (1) to lowest (9):
1. H (Highest)
2. E
3. G
4. A
5. C
6. F
7. D
8. I
9. B (Lowest)
Step 5: Identify the third lowest marks.
Counting from the lowest:
- 1st lowest: B (Position 9)
- 2nd lowest: I (Position 8)
- 3rd lowest: D (Position 7)
Therefore, D scored the third lowest marks in the test.
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