Supervisor's memo: At the present rate of manufacture we will not have the 1,200 circuit boards assembled in time to...
GMAT Two Part Analysis : (TPA) Questions
Supervisor's memo: At the present rate of manufacture we will not have the 1,200 circuit boards assembled in time to ship them to the customer. We currently have 10 workers, working 8 hours a day, assembling the boards, and to date they've assembled 400. In order to finish the customer's order in time, I'll need to have each of the workers work an additional 2 hours for each of the 10 work days between now and the deadline.
One can determine the hourly rate at which each worker assembled circuit boards up to the date of the supervisor's memo by dividing 1 circuit boards by the product of 2 worker-hours and the number of days since the workers began assembling the circuit boards. Select Circuit boards for the option that fills the blank labeled 1 in the given statement, and select Worker-hours for the option that fills the blank labeled 2 in the given statement to create the most accurate statement on the basis of the information provided. Make only two selections, one in each column.
Phase 1: Owning the Dataset
Visual Representation
Let's create a simple table to track our key information:
| Current Status | Values |
| Total boards needed | 1,200 |
| Boards assembled to date | 400 |
| Number of workers | 10 |
| Current hours per day | 8 |
| Worker-hours per day | \(10 \times 8 = 80\) |
Phase 2: Understanding the Question
Breaking Down the Complex Statement
The statement looks intimidating, but let's break it down:
"One can determine the hourly rate at which each worker assembled circuit boards up to the date of the supervisor's memo by dividing [1] circuit boards by the product of [2] worker-hours and the number of days since the workers began assembling the circuit boards."
Key components:
- We want: hourly rate per worker
- Formula structure: \([1] \div ([2] \times \mathrm{days})\)
- [1] must be in units of "circuit boards"
- [2] must be in units of "worker-hours"
What Makes Sense Mathematically
To find hourly rate per worker, we need:
- Total circuit boards assembled ÷ Total worker-hours
- Total worker-hours = Worker-hours per day × Number of days
Phase 3: Finding the Answer
Identifying the Values
For blank 1 (circuit boards):
- We need the total circuit boards assembled to date
- From our data: 400 circuit boards
For blank 2 (worker-hours):
- We need worker-hours per day (since it's multiplied by days)
- From our data: 10 workers × 8 hours/day = 80 worker-hours per day
Verification
Let's verify our formula makes sense:
- Hourly rate per worker = \(400 \div (80 \times d)\) boards per worker-hour
- \(= 400 \div (80d)\) boards per worker-hour
- \(= 5/d\) boards per worker per hour
This is logical because as the number of days (d) increases, the hourly rate decreases, which makes sense.
Phase 4: Solution
Final Answer:
- Blank 1 (Circuit boards): 400
- Blank 2 (Worker-hours): 80
This creates the statement: "One can determine the hourly rate at which each worker assembled circuit boards up to the date of the supervisor's memo by dividing 400 circuit boards by the product of 80 worker-hours and the number of days since the workers began assembling the circuit boards."