A firm interviewed six candidates — U, V, W, X, Y and Z — over three consecutive days, Monday, Tuesday and Wednesday. Exactly two candidates were interviewed each day, one in the morning slot and one in the afternoon slot. Each candidate applied for exactly one of three roles — Analyst, Designer and Manager — and exactly two candidates applied for each role.
The following is known:
1. V was the first candidate to be interviewed, and V did not apply for the Analyst role.
2. U was interviewed in an afternoon slot, on the day immediately after the day of X's interview.
3. W and Y were interviewed on the same day, with W before Y.
4. Both Manager candidates were interviewed in morning slots.
5. No two candidates applying for the same role were interviewed on the same day.
6. X and U applied for the same role.
7. W and V applied for different roles, and Z did not apply for the Designer role.
The following is known:
1. V was the first candidate to be interviewed, and V did not apply for the Analyst role.
2. U was interviewed in an afternoon slot, on the day immediately after the day of X's interview.
3. W and Y were interviewed on the same day, with W before Y.
4. Both Manager candidates were interviewed in morning slots.
5. No two candidates applying for the same role were interviewed on the same day.
6. X and U applied for the same role.
7. W and V applied for different roles, and Z did not apply for the Designer role.
Question 1
Single correct option
Who was interviewed on Tuesday afternoon?
- A. U
- B. X
- C. Z
- D. Y
Show answer and solution
Answer: (A) U
Order: V is Monday morning. If U were Wednesday afternoon, X would be on Tuesday and no day would be free for the W–Y pair; so U is Tuesday afternoon, X is Monday afternoon, W–Y take Wednesday (W morning, Y afternoon) and Z is Tuesday morning.
Roles: Managers are only in mornings (V, Z, W). X and U share a role and are afternoon candidates, so they are both Analysts or both Designers. If both were Designers, V (not Analyst, not Designer) would be a Manager, Y would be the other Analyst, and W (≠ V's role) would be the second Analyst — but W and Y would then share a role on Wednesday, violating clue 5. So X = U = Analyst. Y (afternoon) must then be a Designer, Z (not Designer) is a Manager, and of V and W one is Designer and one Manager; W cannot be Designer (same day as Y), so W = Manager and V = Designer.
| Day | Morning | Afternoon |
|---|---|---|
| Monday | V (Designer) | X (Analyst) |
| Tuesday | Z (Manager) | U (Analyst) |
| Wednesday | W (Manager) | Y (Designer) |
Tuesday afternoon: U.
Roles: Managers are only in mornings (V, Z, W). X and U share a role and are afternoon candidates, so they are both Analysts or both Designers. If both were Designers, V (not Analyst, not Designer) would be a Manager, Y would be the other Analyst, and W (≠ V's role) would be the second Analyst — but W and Y would then share a role on Wednesday, violating clue 5. So X = U = Analyst. Y (afternoon) must then be a Designer, Z (not Designer) is a Manager, and of V and W one is Designer and one Manager; W cannot be Designer (same day as Y), so W = Manager and V = Designer.
| Day | Morning | Afternoon |
|---|---|---|
| Monday | V (Designer) | X (Analyst) |
| Tuesday | Z (Manager) | U (Analyst) |
| Wednesday | W (Manager) | Y (Designer) |
Tuesday afternoon: U.
Question 2
Single correct option
Which role did Y apply for?
- A. Analyst
- B. Designer
- C. Manager
- D. Cannot be determined
Show answer and solution
Answer: (B) Designer
Order: V is Monday morning. If U were Wednesday afternoon, X would be on Tuesday and no day would be free for the W–Y pair; so U is Tuesday afternoon, X is Monday afternoon, W–Y take Wednesday (W morning, Y afternoon) and Z is Tuesday morning.
Roles: Managers are only in mornings (V, Z, W). X and U share a role and are afternoon candidates, so they are both Analysts or both Designers. If both were Designers, V (not Analyst, not Designer) would be a Manager, Y would be the other Analyst, and W (≠ V's role) would be the second Analyst — but W and Y would then share a role on Wednesday, violating clue 5. So X = U = Analyst. Y (afternoon) must then be a Designer, Z (not Designer) is a Manager, and of V and W one is Designer and one Manager; W cannot be Designer (same day as Y), so W = Manager and V = Designer.
| Day | Morning | Afternoon |
|---|---|---|
| Monday | V (Designer) | X (Analyst) |
| Tuesday | Z (Manager) | U (Analyst) |
| Wednesday | W (Manager) | Y (Designer) |
Y applied for the Designer role.
Roles: Managers are only in mornings (V, Z, W). X and U share a role and are afternoon candidates, so they are both Analysts or both Designers. If both were Designers, V (not Analyst, not Designer) would be a Manager, Y would be the other Analyst, and W (≠ V's role) would be the second Analyst — but W and Y would then share a role on Wednesday, violating clue 5. So X = U = Analyst. Y (afternoon) must then be a Designer, Z (not Designer) is a Manager, and of V and W one is Designer and one Manager; W cannot be Designer (same day as Y), so W = Manager and V = Designer.
| Day | Morning | Afternoon |
|---|---|---|
| Monday | V (Designer) | X (Analyst) |
| Tuesday | Z (Manager) | U (Analyst) |
| Wednesday | W (Manager) | Y (Designer) |
Y applied for the Designer role.
Question 3
Single correct option
Which two candidates applied for the Manager role?
- A. V and Z
- B. V and W
- C. X and U
- D. Z and W
Show answer and solution
Answer: (D) Z and W
Order: V is Monday morning. If U were Wednesday afternoon, X would be on Tuesday and no day would be free for the W–Y pair; so U is Tuesday afternoon, X is Monday afternoon, W–Y take Wednesday (W morning, Y afternoon) and Z is Tuesday morning.
Roles: Managers are only in mornings (V, Z, W). X and U share a role and are afternoon candidates, so they are both Analysts or both Designers. If both were Designers, V (not Analyst, not Designer) would be a Manager, Y would be the other Analyst, and W (≠ V's role) would be the second Analyst — but W and Y would then share a role on Wednesday, violating clue 5. So X = U = Analyst. Y (afternoon) must then be a Designer, Z (not Designer) is a Manager, and of V and W one is Designer and one Manager; W cannot be Designer (same day as Y), so W = Manager and V = Designer.
| Day | Morning | Afternoon |
|---|---|---|
| Monday | V (Designer) | X (Analyst) |
| Tuesday | Z (Manager) | U (Analyst) |
| Wednesday | W (Manager) | Y (Designer) |
Managers must be in morning slots (V, Z, W). V is the Designer (not Analyst, and W ≠ V rules out V = Manager in the only consistent case), so the Managers are Z and W.
Roles: Managers are only in mornings (V, Z, W). X and U share a role and are afternoon candidates, so they are both Analysts or both Designers. If both were Designers, V (not Analyst, not Designer) would be a Manager, Y would be the other Analyst, and W (≠ V's role) would be the second Analyst — but W and Y would then share a role on Wednesday, violating clue 5. So X = U = Analyst. Y (afternoon) must then be a Designer, Z (not Designer) is a Manager, and of V and W one is Designer and one Manager; W cannot be Designer (same day as Y), so W = Manager and V = Designer.
| Day | Morning | Afternoon |
|---|---|---|
| Monday | V (Designer) | X (Analyst) |
| Tuesday | Z (Manager) | U (Analyst) |
| Wednesday | W (Manager) | Y (Designer) |
Managers must be in morning slots (V, Z, W). V is the Designer (not Analyst, and W ≠ V rules out V = Manager in the only consistent case), so the Managers are Z and W.
Question 4
Numerical answer
How many candidates were interviewed after the second Analyst candidate's interview?
Show answer and solution
Answer: 2
Order: V is Monday morning. If U were Wednesday afternoon, X would be on Tuesday and no day would be free for the W–Y pair; so U is Tuesday afternoon, X is Monday afternoon, W–Y take Wednesday (W morning, Y afternoon) and Z is Tuesday morning.
Roles: Managers are only in mornings (V, Z, W). X and U share a role and are afternoon candidates, so they are both Analysts or both Designers. If both were Designers, V (not Analyst, not Designer) would be a Manager, Y would be the other Analyst, and W (≠ V's role) would be the second Analyst — but W and Y would then share a role on Wednesday, violating clue 5. So X = U = Analyst. Y (afternoon) must then be a Designer, Z (not Designer) is a Manager, and of V and W one is Designer and one Manager; W cannot be Designer (same day as Y), so W = Manager and V = Designer.
| Day | Morning | Afternoon |
|---|---|---|
| Monday | V (Designer) | X (Analyst) |
| Tuesday | Z (Manager) | U (Analyst) |
| Wednesday | W (Manager) | Y (Designer) |
Analysts: X (Monday afternoon, 2nd slot) and U (Tuesday afternoon, 4th slot). After U come W and Y, so the answer is 2.
Roles: Managers are only in mornings (V, Z, W). X and U share a role and are afternoon candidates, so they are both Analysts or both Designers. If both were Designers, V (not Analyst, not Designer) would be a Manager, Y would be the other Analyst, and W (≠ V's role) would be the second Analyst — but W and Y would then share a role on Wednesday, violating clue 5. So X = U = Analyst. Y (afternoon) must then be a Designer, Z (not Designer) is a Manager, and of V and W one is Designer and one Manager; W cannot be Designer (same day as Y), so W = Manager and V = Designer.
| Day | Morning | Afternoon |
|---|---|---|
| Monday | V (Designer) | X (Analyst) |
| Tuesday | Z (Manager) | U (Analyst) |
| Wednesday | W (Manager) | Y (Designer) |
Analysts: X (Monday afternoon, 2nd slot) and U (Tuesday afternoon, 4th slot). After U come W and Y, so the answer is 2.
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