A company's office building has six floors numbered 1 (lowest) to 6 (highest). Each floor houses exactly one of six departments — HR, Finance, Legal, Sales, IT and Admin. The six departments have 12, 18, 24, 30, 36 and 42 employees, in some order. The following is known:
1. IT is on the floor immediately above HR.
2. Sales has the largest number of employees and is on an even-numbered floor.
3. Legal is on either the top floor or the bottom floor.
4. Finance has exactly twice as many employees as Legal.
5. HR has the fewest employees.
6. The departments on floors 3 and 4 together have 36 employees.
7. IT has fewer employees than Admin.
8. The departments on floors 4, 5 and 6 together have 78 employees.
1. IT is on the floor immediately above HR.
2. Sales has the largest number of employees and is on an even-numbered floor.
3. Legal is on either the top floor or the bottom floor.
4. Finance has exactly twice as many employees as Legal.
5. HR has the fewest employees.
6. The departments on floors 3 and 4 together have 36 employees.
7. IT has fewer employees than Admin.
8. The departments on floors 4, 5 and 6 together have 78 employees.
Question 1
Single correct option
Which department is on floor 5?
- A. IT
- B. Finance
- C. Admin
- D. Legal
Show answer and solution
Answer: (B) Finance
Deduction: HR has 12 and Sales 42. Finance = 2 × Legal allows (12, 24) or (18, 36); 12 belongs to HR, so Legal = 18 and Finance = 36. IT and Admin share 24 and 30; IT < Admin ⇒ IT = 24, Admin = 30.
Floors 3 and 4 hold two departments totalling 36; from 12, 18, 24, 30, 36, 42 the only such pair is 12 + 24 ⇒ HR and IT are on floors 3 and 4, and as IT is directly above HR, HR = 3 and IT = 4.
Floors 4–6 total 78 ⇒ floors 5 and 6 total 54 = 18 + 36 ⇒ Legal and Finance; Legal must be on the top floor ⇒ Legal = 6, Finance = 5. Sales is on an even floor ⇒ 2, and Admin takes floor 1.
| Floor | Department | Employees |
|---|---|---|
| 6 | Legal | 18 |
| 5 | Finance | 36 |
| 4 | IT | 24 |
| 3 | HR | 12 |
| 2 | Sales | 42 |
| 1 | Admin | 30 |
Floors 3 and 4 hold two departments totalling 36; from 12, 18, 24, 30, 36, 42 the only such pair is 12 + 24 ⇒ HR and IT are on floors 3 and 4, and as IT is directly above HR, HR = 3 and IT = 4.
Floors 4–6 total 78 ⇒ floors 5 and 6 total 54 = 18 + 36 ⇒ Legal and Finance; Legal must be on the top floor ⇒ Legal = 6, Finance = 5. Sales is on an even floor ⇒ 2, and Admin takes floor 1.
| Floor | Department | Employees |
|---|---|---|
| 6 | Legal | 18 |
| 5 | Finance | 36 |
| 4 | IT | 24 |
| 3 | HR | 12 |
| 2 | Sales | 42 |
| 1 | Admin | 30 |
Question 2
Numerical answer
How many employees does Admin have?
Show answer and solution
Answer: 30
Deduction: HR has 12 and Sales 42. Finance = 2 × Legal allows (12, 24) or (18, 36); 12 belongs to HR, so Legal = 18 and Finance = 36. IT and Admin share 24 and 30; IT < Admin ⇒ IT = 24, Admin = 30.
Floors 3 and 4 hold two departments totalling 36; from 12, 18, 24, 30, 36, 42 the only such pair is 12 + 24 ⇒ HR and IT are on floors 3 and 4, and as IT is directly above HR, HR = 3 and IT = 4.
Floors 4–6 total 78 ⇒ floors 5 and 6 total 54 = 18 + 36 ⇒ Legal and Finance; Legal must be on the top floor ⇒ Legal = 6, Finance = 5. Sales is on an even floor ⇒ 2, and Admin takes floor 1.
| Floor | Department | Employees |
|---|---|---|
| 6 | Legal | 18 |
| 5 | Finance | 36 |
| 4 | IT | 24 |
| 3 | HR | 12 |
| 2 | Sales | 42 |
| 1 | Admin | 30 |
Floors 3 and 4 hold two departments totalling 36; from 12, 18, 24, 30, 36, 42 the only such pair is 12 + 24 ⇒ HR and IT are on floors 3 and 4, and as IT is directly above HR, HR = 3 and IT = 4.
Floors 4–6 total 78 ⇒ floors 5 and 6 total 54 = 18 + 36 ⇒ Legal and Finance; Legal must be on the top floor ⇒ Legal = 6, Finance = 5. Sales is on an even floor ⇒ 2, and Admin takes floor 1.
| Floor | Department | Employees |
|---|---|---|
| 6 | Legal | 18 |
| 5 | Finance | 36 |
| 4 | IT | 24 |
| 3 | HR | 12 |
| 2 | Sales | 42 |
| 1 | Admin | 30 |
Question 3
Single correct option
Which department is on the floor immediately below HR?
- A. Legal
- B. Sales
- C. Admin
- D. IT
Show answer and solution
Answer: (B) Sales
Deduction: HR has 12 and Sales 42. Finance = 2 × Legal allows (12, 24) or (18, 36); 12 belongs to HR, so Legal = 18 and Finance = 36. IT and Admin share 24 and 30; IT < Admin ⇒ IT = 24, Admin = 30.
Floors 3 and 4 hold two departments totalling 36; from 12, 18, 24, 30, 36, 42 the only such pair is 12 + 24 ⇒ HR and IT are on floors 3 and 4, and as IT is directly above HR, HR = 3 and IT = 4.
Floors 4–6 total 78 ⇒ floors 5 and 6 total 54 = 18 + 36 ⇒ Legal and Finance; Legal must be on the top floor ⇒ Legal = 6, Finance = 5. Sales is on an even floor ⇒ 2, and Admin takes floor 1.
| Floor | Department | Employees |
|---|---|---|
| 6 | Legal | 18 |
| 5 | Finance | 36 |
| 4 | IT | 24 |
| 3 | HR | 12 |
| 2 | Sales | 42 |
| 1 | Admin | 30 |
HR is on floor 3; floor 2 has Sales.
Floors 3 and 4 hold two departments totalling 36; from 12, 18, 24, 30, 36, 42 the only such pair is 12 + 24 ⇒ HR and IT are on floors 3 and 4, and as IT is directly above HR, HR = 3 and IT = 4.
Floors 4–6 total 78 ⇒ floors 5 and 6 total 54 = 18 + 36 ⇒ Legal and Finance; Legal must be on the top floor ⇒ Legal = 6, Finance = 5. Sales is on an even floor ⇒ 2, and Admin takes floor 1.
| Floor | Department | Employees |
|---|---|---|
| 6 | Legal | 18 |
| 5 | Finance | 36 |
| 4 | IT | 24 |
| 3 | HR | 12 |
| 2 | Sales | 42 |
| 1 | Admin | 30 |
HR is on floor 3; floor 2 has Sales.
Question 4
Numerical answer
What is the total number of employees on floors 1, 2 and 3 taken together?
Show answer and solution
Answer: 84
Deduction: HR has 12 and Sales 42. Finance = 2 × Legal allows (12, 24) or (18, 36); 12 belongs to HR, so Legal = 18 and Finance = 36. IT and Admin share 24 and 30; IT < Admin ⇒ IT = 24, Admin = 30.
Floors 3 and 4 hold two departments totalling 36; from 12, 18, 24, 30, 36, 42 the only such pair is 12 + 24 ⇒ HR and IT are on floors 3 and 4, and as IT is directly above HR, HR = 3 and IT = 4.
Floors 4–6 total 78 ⇒ floors 5 and 6 total 54 = 18 + 36 ⇒ Legal and Finance; Legal must be on the top floor ⇒ Legal = 6, Finance = 5. Sales is on an even floor ⇒ 2, and Admin takes floor 1.
| Floor | Department | Employees |
|---|---|---|
| 6 | Legal | 18 |
| 5 | Finance | 36 |
| 4 | IT | 24 |
| 3 | HR | 12 |
| 2 | Sales | 42 |
| 1 | Admin | 30 |
Floors 1–3: Admin 30 + Sales 42 + HR 12 = 84. (Check: total 162 − floors 4–6 (78) = 84 ✓.)
Floors 3 and 4 hold two departments totalling 36; from 12, 18, 24, 30, 36, 42 the only such pair is 12 + 24 ⇒ HR and IT are on floors 3 and 4, and as IT is directly above HR, HR = 3 and IT = 4.
Floors 4–6 total 78 ⇒ floors 5 and 6 total 54 = 18 + 36 ⇒ Legal and Finance; Legal must be on the top floor ⇒ Legal = 6, Finance = 5. Sales is on an even floor ⇒ 2, and Admin takes floor 1.
| Floor | Department | Employees |
|---|---|---|
| 6 | Legal | 18 |
| 5 | Finance | 36 |
| 4 | IT | 24 |
| 3 | HR | 12 |
| 2 | Sales | 42 |
| 1 | Admin | 30 |
Floors 1–3: Admin 30 + Sales 42 + HR 12 = 84. (Check: total 162 − floors 4–6 (78) = 84 ✓.)
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