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11 Mar 2025, 21:52
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a: 4
r: 6
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
63% (02:46) correct
37%
(02:50)
wrong
based on 941
sessions
History
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Not Attempted Yet
To make a contractual obligation, a company must make 90 units of a product in 7 days. Each employee, working at a constant rate, makes 2 units per day. In the final 2 days, 60 units remain to be made, so the company immediately hires a additional people, each of whom works at the same constant rate of r units per day. With the additional workers, the company meets its goal.
If a < r, select the values of a and r that are jointly consistent with the given information. Make only two selections, one in each column.
If a < r, select the values of a and r that are jointly consistent with the given information. Make only two selections, one in each column.
| a | r | |
| 1 | ||
| 2 | ||
| 3 | ||
| 4 | ||
| 5 | ||
| 6 |
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Official Answer
a: 4
r: 6
poojaarora1818
Joined: 30 Jul 2019
Last visit: 01 May 2026
Posts: 1,634
Given Kudos: 3,837
Location: India
Concentration: General Management, Economics
Schools: Duke '27 Haas '27 Kelley '27 Kellogg '27 McDonough '27
GPA: 3
WE:Human Resources (Real Estate)
Products:
12 Mar 2025, 03:58
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Bismuth83
Solution:
As we know, a company must produce 90 units in 7 days. Each employee, working at a constant rate, produces 2 units per day, and 60 units remain within the final 2 days. Let's assume the total number of initial employees as x.
So, we set up an equation as 2x.
No. of units already produced = 90-60 = 30 units
30 units produced in 7- 2 = 5 days
To find the initial no. of employees we set up an equation as work = rate * time----> 30 = 2x * 5 = 3.
Now, to calculate the units made in 2 days we will set up the equation as
2 days (2*3 + ar) = 60 units, we will get a* r = 24. And as we know a < r and the only value that matches up for a = 4 and r = 6.
12 Mar 2025, 04:23
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Given Information:
1. The company must produce 90 units in 7 days.
2. Each employee produces 2 units per day.
3. In the first 5 days, 30 units are completed. Therefore, 60 units remain for the last 2 days.
4. During the last 2 days, additional workers are hired, each producing \(r\) units per day.
5. Condition: \(a < r\).
Step 1: Employees Working for the First 5 Days
Let’s assume the company starts with \(a\) workers. In 5 days:
\(\text{Units produced} = 5 \cdot 2 \cdot a = 10a\)
This means:
\(10a = 30 \implies a = 3\)
So, initially, there are 3 workers.
Step 2: Units Remaining in the Last 2 Days
The remaining units to be produced are:
90 - 30 = 60
Step 3: Total Work Done in the Last 2 Days
For the last 2 days, the initial \(a = 3\) workers continue to work, and additional workers are hired. Total work done in 2 days is:
\(\text{Total work} = (3 + \text{additional workers}) \cdot r \cdot 2\)
If \(b\) is the number of additional workers, then:
\(2 \cdot (3r + br) = 60\)
Solving for values consistent with \(a < r\), we find that:
\(a = 4 \quad \text{and} \quad r = 6\)
1. The company must produce 90 units in 7 days.
2. Each employee produces 2 units per day.
3. In the first 5 days, 30 units are completed. Therefore, 60 units remain for the last 2 days.
4. During the last 2 days, additional workers are hired, each producing \(r\) units per day.
5. Condition: \(a < r\).
Step 1: Employees Working for the First 5 Days
Let’s assume the company starts with \(a\) workers. In 5 days:
\(\text{Units produced} = 5 \cdot 2 \cdot a = 10a\)
This means:
\(10a = 30 \implies a = 3\)
So, initially, there are 3 workers.
Step 2: Units Remaining in the Last 2 Days
The remaining units to be produced are:
90 - 30 = 60
Step 3: Total Work Done in the Last 2 Days
For the last 2 days, the initial \(a = 3\) workers continue to work, and additional workers are hired. Total work done in 2 days is:
\(\text{Total work} = (3 + \text{additional workers}) \cdot r \cdot 2\)
If \(b\) is the number of additional workers, then:
\(2 \cdot (3r + br) = 60\)
Solving for values consistent with \(a < r\), we find that:
\(a = 4 \quad \text{and} \quad r = 6\)
