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.

Four of the following five are alike in a certain way and hence form a group. Find the one who doesn’t belong to the group?

The correct answer is Q-S.

Step-by-Step Explanation and Derivation:

1. Determine the sequential order of all 9 persons (Positions 1 to 9):

• Clue: "L purchase product just after K."
This means K and L are together in consecutive positions: (K, L).

• Clue: "Three persons purchase products between K and M" and "R purchase product two persons before M."
Since R is two positions before M, the arrangement around M is: R, _, M.
Placing K, L three persons before M yields the relative order: K, L, R, _, M (where K is at position x, L at x+1, R at x+2, and M at x+4).

• Clue: "Four persons purchase product between L and Q."
Four persons between L and Q means Q is 5 positions away from L. Since L is at x+1, Q must be at position (x+1) + 5 = x+6.

• Clue: "The number of persons purchases products before K is same as the number of persons purchase products after Q."
If K is at position x, the number of persons before K is x - 1.
If Q is at position x + 6, the number of persons after Q is 9 - (x + 6) = 3 - x.
Equating both: x - 1 = 3 - x ⇒ 2x = 4 ⇒ x = 2.

Therefore:
• Position 2 = K
• Position 3 = L
• Position 4 = R
• Position 6 = M
• Position 8 = Q

2. Placing the remaining persons:

• Clue: "Two persons purchase product between R and O who purchase product before K."
R is at position 4. Two persons before R gives position 1 for O (which is indeed before K).

• Clue: "P purchase product before S but after M."
The open positions after M (position 6) are 7 and 9 (since Q is at 8).
Placing P before S gives position 7 for P and position 9 for S.

• The only remaining empty spot is position 5, which must be filled by N.

Final Sequential Order (1 to 9):

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

3. Analyze the options to find the odd one out:

• O-L: There is exactly 1 person (K) between O and L.
• K-R: There is exactly 1 person (L) between K and R.
• L-N: There is exactly 1 person (R) between L and N.
• M-Q: There is exactly 1 person (P) between M and Q.
• Q-S: Q and S purchase products immediately one after another (0 persons between them).

Hence, Q-S does not belong to the group.