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.

Which among the following statement is not true?

To find which statement is not true, we first determine the ordering of the eight persons based on the given conditions:

1. L buys immediately before Q: This gives the consecutive pair $L,Q$.
2. O buys two persons before Q: This means there is exactly one person between O and Q. Since L is immediately before Q, the order is $O,L,Q$.
3. As many persons buy between O and Q as between L and K: Since there is 1 person between O and Q, there must be 1 person between L and K.
4. K buys before O: Since K is before O, and there is 1 person (O) between L and K, K must immediately precede O. This gives the sequence $K,O,L,Q$.
5. Two persons buy between K and P: Since K is followed by O and L, P must buy before K. With exactly two persons between them, the sequence becomes $P,\_,\_,K,O,L,Q$.
6. Two persons buy between M and L: Since L is at index 6 in our sequence, M must be at index 3 (which is $6-3$). This fits into the sequence: $P,\_,M,K,O,L,Q,\_$.
7. J buys before N and after P: The remaining empty spots are at positions 2 and 8. Since J buys before N, J must be at position 2 and N must be at position 8.

Thus, the final buying order from 1 to 8 is:
1. P
2. J
3. M
4. K
5. O
6. L
7. Q
8. N

Now we evaluate the given options:

• "P buys the first among all": True, P is at position 1.
• "J buys just before M": True, J is at 2 and M is at 3.
• "Odd number of persons buys after O": True, three persons (L, Q, N) buy after O.
• "N buys at least before one person": False, since N is at position 8 and is the last person to buy.