Directions: Read the information and answer the given questions.
Nine individuals, namely, X, Y, Z, P, Q, R, S, T, and U, are purchasing different products at a store counter, one after another, but not necessarily in the same order.
As many individuals purchase between Q and R as between X and Y. At most two individuals purchase between Q and R, who purchase before Q. Only one individual purchases between R and P, who purchases immediately after X. Z purchases three after Y. Q purchases three before S. More than three individuals purchase between T and U, who purchase after T.
Who among the following purchases two products before X?
- AOption (a)
The one who purchases immediately after Y
- BOption (b)
Z
- COption (c)
T
- DOption (d)
The one who purchases three products before Z
- EOption (e)
Y
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Correct answer
T
Why this answer is correct
1. Q purchases three before S. 2. At most two individuals purchase between Q and R, who purchases before Q.
Here, we have 3 Cases, i.e., Case 1, Case 2, and Case 3.
| Persons | ||
|---|---|---|
| Case 1 | Case 2 | Case 3 |
| R | R | R |
| Q | ||
| Q | ||
| Q | ||
| S | ||
| S | ||
| S |
3. Only one individual purchases between R and P, who purchase immediately after X.
Here, we have 6 cases, i.e., 2 more subcases of Case 1 and 1 more subcase of Case 3.
| Persons | |||||
|---|---|---|---|---|---|
| Case 1 | Case 1a | Case 1b | Case 2 | Case 3 | Case 3a |
| R | X | X | |||
| X | R | P | P | X | |
| P | X | R | P | ||
| Q | P | X | R | R | |
| Q | P | Q | R | ||
| Q | Q | Q | |||
| S | |||||
| S | S | ||||
| S | S | S |
- As many individuals purchase between Q and R as between X and Y.
Now, we can eliminate Case 3. (Because there is no vacant place for Y)
| Persons | ||||
|---|---|---|---|---|
| Case 1 | Case 1a | Case 1b | Case 2 | Case 3a |
| R | Y/ | X | Y | |
| X | R | P | X | |
| P | X | R | Y | P |
| Q | P | X | R | |
| Y | Q | P | R | |
| Y | Q | Q | Q | |
| S | Y/ | |||
| S | ||||
| S | S | S |
- Z purchases three after Y.
Now, we can eliminate Case 1b and Case 2.
| Persons | ||
|---|---|---|
| Case 1 | Case 1a | Case 3a |
| R | Y | |
| X | R | X |
| P | X | P |
| Q | P | Z |
| Y | Q | R |
| Y | Q | |
| S | ||
| Z | S | |
| Z | S |
- More than three individuals purchase between T and U, who purchase after T.
Now, we can eliminate Case 1 and Case 3a.
This is our final arrangement,
| Persons |
|---|
| Case 1a |
| T |
| R |
| X |
| P |
| Q |
| Y |
| U |
| S |
| Z |
Hence, the correct answer is T.