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.

How many persons purchase products between O and P?

Correct Answer: Five

Step-by-step Explanation and Solution:

To determine how many persons purchase products between O and P, let us carefully analyze the given conditions step-by-step and determine the exact order of all 9 persons (positions 1 to 9, from first to last).

1. Analyze the given clues:

• Total number of persons = 9.

• Three persons purchase products between K and M.

• R purchases product two persons before M (which means: R _ M, i.e., R is 2 positions above M).

• Two persons purchase product between R and O.

• O purchases product before K (O ... K).

• L purchases product just after K (K L).

• Four persons purchase product between L and Q.

• The number of persons purchasing products before K is the same as the number of persons purchasing products after Q.

• P purchases product before S but after M (M ... P ... S).

2. Determining the positions of K, L, and Q:

Let K be at position k (1-indexed, from 1 to 9). Then L is at position k + 1.

Number of persons before K = k - 1.

Thus, number of persons after Q must also be k - 1.

This means Q is at position: 9 - (k - 1) = 10 - k.

We are given that four persons purchase between L (at k + 1) and Q (at 10 - k).

So, |(10 - k) - (k + 1)| - 1 = 4

⇒ |9 - 2k| = 5

This gives two possibilities:

• Case 1: 9 - 2k = 5 ⇒ 2k = 4 ⇒ k = 2.

• Case 2: 9 - 2k = -5 ⇒ 2k = 14 ⇒ k = 7.

Testing Case 1 (k = 2):

If K is at position 2, then L is at position 3, and Q is at position 8.

Since 3 persons purchase between K and M, M must be at position 2 + 4 = 6.

R purchases product two persons before M, so R is at position 4.

Two persons purchase between R (position 4) and O. So O could be at position 1 or position 7.

However, O must purchase before K (position 2), so O must be at position 1.

Let's check the remaining clues:

• M is at position 6.

• P purchases after M (positions left: 5, 7, 9).

• P is before S, so P can be at position 7 and S at position 9, leaving N at position 5.

Let's verify all positions for Case 1:

Position 1: O

Position 2: K

Position 3: L

Position 4: R

Position 5: N

Position 6: M

Position 7: P

Position 8: Q

Position 9: S

Verification of conditions:

1. 3 persons between K(2) and M(6): L, R, N (Valid)

2. R(4) is 2 persons before M(6) (Valid)

3. 2 persons between R(4) and O(1): K, L (Valid)

4. O(1) purchases before K(2) (Valid)

5. L(3) purchases just after K(2) (Valid)

6. 4 persons between L(3) and Q(8): R, N, M, P (Valid)

7. Persons before K(2) = 1 (O); Persons after Q(8) = 1 (S) (Valid)

8. P(7) is after M(6) and before S(9) (Valid)

3. Answer the Question:

O is at Position 1 and P is at Position 7.

The persons between O and P are at positions 2, 3, 4, 5, and 6 (K, L, R, N, M).

Therefore, there are 5 (Five) persons purchasing products between O and P.