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.
How many students scored lower than C?
Correct Answer :
Four
Solution :
The correct option is Four.
Let us arrange the nine students in descending order of their marks from rank 1 (highest mark) to rank 9 (lowest mark), based on the clues given in the question.
Step 1: Analyze the statements about ranks and positions.
1. There are 9 students total.
2. "G's score is immediately lower than E's score."
This means E and G are placed together in adjacent positions, with E higher than G: (E, G).
3. "I's score is immediately higher than B's score and immediately lower than D's score."
This gives a continuous block of three students: (D, I, B).
4. "Five students scored marks between E and I."
Since there are 5 students between E and I, the difference between their rank positions must be 6 (i.e., if E is at position x, I is at position x + 6 or vice versa).
5. "Three students scored marks between G and D."
Since G is immediately after E, let us test placing E before I:
If E is at rank 1, then G is at rank 2.
With 5 students between E and I (ranks 2, 3, 4, 5, 6), I must be at rank 7.
Since (D, I, B) are consecutive, D would be at rank 6 and B at rank 8.
Let us check the condition "Three students scored marks between G (rank 2) and D (rank 6)": Ranks 3, 4, and 5 are between rank 2 and rank 6, which is exactly 3 students. This perfectly matches!
Step 2: Determine the positions of all students.
So far, we have the following positions:
Rank 1: E
Rank 2: G
Rank 6: D
Rank 7: I
Rank 8: B
Now let's place the remaining students: H, A, C, F.
6. "H scored a higher score than E."
Wait, if H scored higher than E, H must take Rank 1, pushing E to Rank 2 and G to Rank 3.
Let me re-verify the positions with H at Rank 1:
Rank 1: H
Rank 2: E
Rank 3: G
Five students between E (rank 2) and I means I is at rank 8 (students at 3, 4, 5, 6, 7 are between them).
Since D is immediately above I, D is at rank 7.
Since B is immediately below I, B is at rank 9.
Check students between G (rank 3) and D (rank 7): ranks 4, 5, and 6 are between them, which is exactly 3 students! This works perfectly.
Let's summarize the confirmed ranks so far:
Rank 1: H
Rank 2: E
Rank 3: G
Rank 7: D
Rank 8: I
Rank 9: B
Remaining open positions are ranks 4, 5, and 6, which must be occupied by A, C, and F.
Step 3: Place A, C, and F in ranks 4, 5, and 6.
7. "A scored higher than C but lower than G."
8. "F scored lower than C but higher than D."
Combining these relative scores: G > A > C > F > D.
Therefore, among the available ranks (4, 5, 6):
Rank 4: A
Rank 5: C
Rank 6: F
Step 4: Final Complete Order of Students (Highest to Lowest):
1. H
2. E
3. G
4. A
5. C
6. F
7. D
8. I
9. B
Step 5: Answer the Question.
The question asks: "How many students scored lower than C?"
C is at rank 5. The students who scored lower than C are F (rank 6), D (rank 7), I (rank 8), and B (rank 9).
Counting them gives exactly 4 students (F, D, I, B).
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