Directions (81-85): Study the following information carefully and answer the questions given below:
Eight persons buy different things one after other. Two persons buy between M and L who buys immediately before Q. O buys two persons before Q. As many persons buy between O and Q as between L and K. K buys before O. Two persons buy between K and P. J buys before N and after P.
The number of persons buys before M is one less than the number of persons buys after ____.
Correct Answer :
O
Solution :
To find the correct answer, we can reconstruct the order of the eight persons buying things one after another step-by-step from the given clues:
Step 1: Analyze the clues for L, Q, and O
- "L buys immediately before Q." This gives us the consecutive block: L, Q.
- "O buys two persons before Q." This means there is exactly one person between O and Q. Since L is immediately before Q, O must be immediately before L, giving us the block: O, L, Q.
Step 2: Position of K
- "As many persons buy between O and Q as between L and K." There is 1 person (L) between O and Q. Therefore, there must be exactly 1 person between L and K.
- "K buys before O." Since K buys before O, K must be placed before the O, L, Q block, separated from L by exactly 1 person (O). This gives us the consecutive block of four persons: K, O, L, Q.
Step 3: Position of P
- "Two persons buy between K and P." This means P can be 3 positions before K or 3 positions after K.
- If P were 3 positions after K, it would occupy the position of Q (since Q is 3 positions after K in the block K, O, L, Q). Thus, P must be 3 positions before K. This gives us the sequence: P, _, _, K, O, L, Q (consisting of 7 positions).
Step 4: Position of M
- "Two persons buy between M and L." In our 7-person sequence, L is at the 6th position from the left. M must be 3 positions away from L.
- If M were 3 positions to the right of L, the sequence would exceed the limit of 8 persons. Thus, M must be 3 positions to the left of L, which corresponds to the 3rd position from the left: P, _, M, K, O, L, Q.
Step 5: Position of J and N
- "J buys before N and after P."
- There is only one empty slot within the 7-person sequence (between P and M). To accommodate both J and N such that J is after P and before N, J must fill this empty slot, and N must be placed at the 8th position at the very end of the sequence.
- This completes the sequence of 8 persons from 1st to 8th:
1. P
2. J
3. M
4. K
5. O
6. L
7. Q
8. N
Step 6: Answer the question
- The number of persons who buy before M (position 3) is 2 (P and J).
- The question states: "The number of persons buys before M is one less than the number of persons buys after ____."
- Since the number of persons buying before M is 2, the number of persons buying after the target person must be:
Therefore, the correct option is O.
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