Nineteen lamps must be connected to a single electric outlet. Each extension…
2010
Nineteen lamps must be connected to a single electric outlet. Each extension cord has four outlets, and each additional cord must occupy one available outlet to extend the connection. What is the minimum number of extension cords required?
Answer: C. 6 — ConceptWhen identical multi-outlet extension cords are connected from one source, each cord supplies several outlets but the connection to the next cord…
- A.
4
- B.
5
- C.
6
- D.
7
Attempted by 1 students.
Show answer & explanation
Correct answer: C
Concept
When identical multi-outlet extension cords are connected from one source, each cord supplies several outlets but the connection to the next cord consumes one of the outlets already created.
If each cord has k outlets, the first cord offers k outlets and every later cord increases the usable total by k − 1. Thus n cords provide k + (n − 1)(k − 1) usable outlets.
Application
Here k = 4, so n cords provide 4 + (n − 1) × 3 usable outlets.
Simplify the capacity: 4 + 3n − 3 = 3n + 1.
Require enough outlets for 19 lamps: 3n + 1 ≥ 19.
Subtract 1 from both sides: 3n ≥ 18.
Divide by 3: n ≥ 6. Therefore the minimum number of extension cords is 6.
Cross-check
Five cords provide 3 × 5 + 1 = 16 usable outlets, which is insufficient, while six cords provide 3 × 6 + 1 = 19, exactly enough. Hence the minimum is 6.