Question: An automated manufacturing plant uses robots to manufacture products. A generation-I robot working alone can manufacture a product in 30 hours whereas a generation-II robot working alone can manufacture the same product in 20 hours. If the manager of the plant wants the product manufacturing time to be greater than equal to 5 hours with at least 1 robot each of both generations working together, how many possible combinations of the number of robots of each generation is possible?

1. 4
2. 5
3. 6
4. 7
5. 8

“An automated manufacturing plant uses robots to manufacture products''- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This GMAT Problem Solving question has been borrowed from the book “GMAT Official Guide 2021”. GMAT quant section mainly tests the rational understanding of the candidates regarding basic maths concepts. The candidates must analyse and interpret the quantitative problems with valid logic and accurate calculations. The candidates must have a strong understanding of numerical calculations in order to crack GMAT Problem Solving questions. The mathematical problems of the GMAT Quant topic in the problem-solving part can be solved by the candidates having better skills in mathematics.

Solution and Explanation:

Approach Solution 1:

The problem statement informs that:

Given:

• An automated manufacturing plant uses robots to manufacture products.
• Generation-I robot alone can manufacture a product in 30 hours.
• Generation-II robot alone can manufacture the same product in 20 hours.
• The manager wants the product manufacturing time to be greater than or equal to 5 hours with at least 1 robot for each of both generations working together.

Find Out:

• The number of possible combinations of the number of robots of each generation is possible.

Let the number of Gen I robots used be x and the number of Gen II robots used be y.
Let the value of x and y will be positive integers. (since it is given that at least 1 robot for each of both generations to be employed)

Given, 1 Generation-I robot takes 30 hr to make the product.
Therefore, the parts of the product produced in 1 hr = 1/30
Then, the x Generation-I robot will make x/30 parts in 1 hr.

In the same way, y Generation-II robots will make y/20 parts in 1 hr.

Therefore in 1 hour, x Generation-I and y Generation-II robots will make x/30 + y/20 robots that can be derived as (3x + 2y)/60
It is stated in the question that the manufacturing time needs to be greater than or equal to 5 hr
Therefore, we can write (3x + 2y)/60 ≤ 1/5
=> 3x + 2y ≤ 12

Therefore, when the value of x = 1, y can have 4 values (1 to 4)
Therefore, when the value of x = 2, y can have 3 values (1 to 3)
Therefore, when the value of x = 3, y can have only 1 value (1)
Thus, the number of possible combinations of the number of robots of each generation = 8

Correct Answer: (E)

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