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 analyze the given statements step-by-step to arrange the 9 students in descending order of their marks (from highest rank 1 to lowest rank 9):
1. "I's score is immediately higher than B's score and immediately lower than D's score."
This gives a fixed block of 3 students in order: D > I > B.
2. "Five students scored marks between E and I."
Since there are 5 students between E and I, there are a total of 7 positions involved from E to I.
Case A: E is above I, so the order is E, _, _, _, _, _, I.
Case B: I is above E, so the order is I, _, _, _, _, _, E.
3. "G's score is immediately lower than E's score."
This means E > G (they are adjacent).
4. "Three students scored marks between G and D."
Let us test Case A: E > G.
Positioning relative to E: E (1st of this group), G (2nd of this group).
If there are 3 students between G and D, then D must be 4 positions away from G.
If D is below G: E, G, _, _, _, D. Since D > I > B, the sequence becomes E, G, _, _, _, D, I, B.
Let's count the total students in this sequence: E (1), G (2), _ (3), _ (4), _ (5), D (6), I (7), B (8).
Notice that between E and I, there are exactly 5 students: G, _, _, _, D. This perfectly satisfies "Five students scored marks between E and I"!
5. "H scored a higher score than E."
So, H is placed above E: H > E.
Let's count positions from the top so far:
1: H
2: E
3: G
4: _
5: _
6: _
7: D
8: I
9: B
6. "A scored higher than C but lower than G." and "F scored lower than C but higher than D."
This gives the relative order between G and D:
G > A > C > F > D.
Since positions 4, 5, and 6 between G (position 3) and D (position 7) are vacant, we place A, C, and F into positions 4, 5, and 6 respectively.
Thus, the complete ranking from highest score to lowest score (1 to 9) is:
1. H
2. E
3. G
4. A
5. C
6. F
7. D
8. I
9. B
Now, let's answer the question: "How many students scored lower than C?"
The students who scored lower than C are F, D, I, and B.
Therefore, exactly 4 students scored lower than C.
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