Directions (96-100): Study the following information carefully and answer the questions given below.

Nine persons-K, L, M, N, O, P, Q, R and S purchase different products one after another but not necessarily in the same order. Three persons purchase products between K and M. R purchase product two persons before M. Two persons purchase product between R and O who purchase product before K. L purchase product just after K. Four persons purchase product between L and Q. The number of persons purchases products before K is same as the number of persons purchase products after Q. P purchase product before S but after M.

Which among the following statement(s) is/are true?
I. S purchase product before K
II. No one purchase product before O
III. More than three persons purchase products after R

The correct answer is Both II and III.

Step-by-step Explanation:

Let us analyze the given information step-by-step to determine the exact order of purchasing products for the nine persons (positions 1 to 9 from first to last):

1. "R purchase product two persons before M":
This means there is exactly 1 person between R and M, with R purchasing before M (i.e., R, _, M).

2. "Two persons purchase product between R and O who purchase product before K":
Since O purchases before K and we need to fit everyone, let us analyze the positions of O, R, M, K, L, and Q.

3. "L purchase product just after K":
This gives the pair (K, L).

4. "The number of persons purchases products before K is same as the number of persons purchase products after Q" and "Four persons purchase product between L and Q":
Let us place O at position 1 (first person to purchase):
- Position 1: O
- Since two persons purchase between R and O, R is at position 4.
- Since R is two persons before M (one person between R and M), M is at position 6.
- Three persons purchase between K and M: since M is 6th, K must be at position 2 (since position 10 does not exist for 9 persons).
- L purchases just after K, so L is at position 3.
- Let's check: K is at position 2, so 1 person purchases before K. Thus, 1 person must purchase after Q, which puts Q at position 8.
- Four persons purchase between L (position 3) and Q (position 8): positions 4, 5, 6, 7 are between them, which is exactly 4 persons!

5. "P purchase product before S but after M":
The remaining positions to fill are 5, 7, and 9 for the remaining persons P, S, and N.
M is at position 6, and P purchases after M and before S.
Thus, P is at position 7 and S is at position 9.
The remaining person N takes position 5.

The complete sequence from 1st to 9th is:

1. O
2. K
3. L
4. R
5. N
6. M
7. P
8. Q
9. S

Now, let us evaluate the given statements:

- Statement I: S purchase product before K
S is at position 9 and K is at position 2. So, S purchases after K. (False)

- Statement II: No one purchase product before O
O is at position 1, so no one purchases product before O. (True)

- Statement III: More than three persons purchase products after R
R is at position 4. The persons purchasing after R are N (5), M (6), P (7), Q (8), and S (9), which is 5 persons (more than 3). (True)

Therefore, statements II and III are true.