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.

How many persons buy between M and N?

To find the number of persons who buy between M and N, let us analyze the given clues step-by-step to determine the correct order of the eight persons buying things one after the other.

Let the positions of the eight persons from first to last be represented by 1 to 8.

Step 1: Analyze the clues.
1. Two persons buy between M and L.
2. L buys immediately before Q. This can be represented as the pair (L, Q).
3. O buys two persons before Q. "Two persons before Q" means there is one person between O and Q. Since L is immediately before Q, O must buy immediately before L. Thus, we have the sequence: O, L, Q.
4. As many persons buy between O and Q as between L and K.
From our sequence, the number of persons between O and Q is exactly one (which is L).
Therefore, the number of persons between L and K must also be exactly one.
Since K buys before O, K cannot be after L. So K must be placed before L. With one person between L and K, and since O is immediately before L, the sequence becomes: K, O, L, Q.
5. Two persons buy between K and P. Since K is at the start of our sequence, let's look at the positions. K, O, L, Q occupy 4 consecutive positions.
If K is at position 1, then the positions are: K(1), O(2), L(3), Q(4).
If K is at position 2, then the positions are: K(2), O(3), L(4), Q(5), and so on.
Since two persons buy between K and P, P can buy either before K or after K. Let's trace the possibilities:
Case A: P buys after K. There are two persons between K and P, so P must be in the position after O and L. Thus, P is at the 4th position relative to K. The sequence becomes: K, O, L, P, Q. But we already know Q is immediately after L, so P cannot be between L and Q. Therefore, P must be after Q. Since there are 2 persons between K and P, the positions relative to K are: K (1st), [O (2nd), L (3rd)], P (4th). This means P is at the position of Q, which is a contradiction. Hence, P must be further down or before K.
Wait, let's recount: K, _, _, P. The two persons between K and P are O and L. So P must be immediately after L? No, the order is K, O, L, Q. Here, between K and Q, there are two persons (O and L). Therefore, Q is the person who is 3rd after K (i.e., two persons between K and Q are O and L). Since the clue says "Two persons buy between K and P", it means P must be in the position of Q. But Q is already there. Thus, P cannot be after K in this consecutive block. P must be before K.
If P is before K, then: P, _, _, K. Here, there are two positions between P and K. This means K is the 4th position after P.

Step 2: Combine the positions.
Let's represent the sequence with P and K: P, _, _, K, O, L, Q.
This sequence contains 7 positions: P(1), empty(2), empty(3), K(4), O(5), L(6), Q(7).
Since there are 8 persons in total, this sequence can fit into the 8 positions in two ways:
Case 1: P is at position 1.
Positions: P(1), 2, 3, K(4), O(5), L(6), Q(7), 8.
Case 2: P is at position 2.
Positions: 1, P(2), 3, 4, K(5), O(6), L(7), Q(8).

Let's test Case 1: P(1), 2, 3, K(4), O(5), L(6), Q(7), 8.
- Clue: "Two persons buy between M and L".
L is at position 6. Two persons between M and L means M can be at position 3 (between 3 and 6, there are 4 and 5, which are K and O - exactly two persons) or position 9 (out of bounds). So, M must be at position 3.
The positions become: P(1), 2, M(3), K(4), O(5), L(6), Q(7), 8.
- Clue: "J buys before N and after P".
The remaining empty positions are 2 and 8.
Since J buys after P (P is at 1) and before N, J must be at position 2 and N must be at position 8.
This satisfies all conditions. Let's write down the final arrangement for Case 1:
1. P
2. J
3. M
4. K
5. O
6. L
7. Q
8. N

Let's double check Case 2: 1, P(2), 3, 4, K(5), O(6), L(7), Q(8).
L is at position 7. Two persons between M and L means M must be at position 4. So: 1, P(2), 3, M(4), K(5), O(6), L(7), Q(8).
Now we need to place J and N. J buys after P and before N. The remaining empty positions are 1 and 3. Since J must buy after P(2), J cannot be at position 1. If J is at position 3, then N must be after J. But the only remaining position is 1, which is before J. Thus, Case 2 is not possible.

Step 3: Count the number of persons between M and N.
From the final correct arrangement:
M is at position 3.
N is at position 8.
The persons between M (3) and N (8) are at positions 4, 5, 6, and 7, which are K, O, L, and Q.
Therefore, there are exactly Four persons buying between M and N.