An automated assembly device simultaneously installs capacitors and resistors on circuit boards of a particular design and size. The device...

Phase 1: Owning the Dataset

Understanding the Assembly Process

Let's create a simple timeline showing what happens in 1 minute:

Time: 0 seconds -------------------------> 60 seconds
      |                                   |
      Start                               Complete 4 boards

Rates:

• Capacitors: 2 per second
• Resistors: 4 per 10 seconds = 0.4 per second

Key Information Table

Phase 2: Understanding the Question

We need to find:

• Statement 1 (Capacitors): Number of capacitors on EACH circuit board
• Statement 2 (Resistors): Number of resistors on EACH circuit board

Key insight: The device works for 1 minute (60 seconds) and completes exactly 4 circuit boards. This means we can calculate total components installed, then divide by 4.

Phase 3: Finding the Answer

Calculating Total Components in 60 Seconds

Capacitors:

• Rate: 2 per second
• Time: 60 seconds
• Total capacitors = \(2 \times 60 = 120\) capacitors

Resistors:

• Rate: 4 per 10 seconds = 0.4 per second
• Time: 60 seconds
• Total resistors = \(0.4 \times 60 = 24\) resistors

Components Per Circuit Board

Since 4 circuit boards are completed:

Capacitors per board:
\(120 \div 4 = 30\) capacitors per board

Resistors per board:
\(24 \div 4 = 6\) resistors per board

Verification with Answer Choices

Looking at our choices: ["6","8","16","24","30","96"]

• Capacitors per board: 30 ✓ (available in choices)
• Resistors per board: 6 ✓ (available in choices)

Phase 4: Solution

Final Answer:

• Capacitors: 30
• Resistors: 6

Each circuit board requires 30 capacitors and 6 resistors. When the device works at maximum capacity for 60 seconds, it installs exactly the right amount to complete 4 boards.