A Manufacturing Company is Testing out a New Design for One of its Most Popular Products GMAT Problem Solving

Question: A manufacturing company is testing out a new design for one of its most popular products. For the test run, the company currently has an inventory of 3,500 widgets and 2000 sprockets. The design requires 3 sprockets and 7 widgets, and the company will produce as many units of the new design as current inventory allows.

In the table below, select one value for the number of sprockets used and one value for the number of units produced.

Correct Answer: (C) for the number of Sprockets; (A) for the number of Units produced

Solution and Explanation:

Approach Solution 1:

The problem statement informs that:
Given:

• A manufacturing company testing out a new design for one of its most popular products.
• For the test run, the company currently has an inventory of 3,500 widgets and 2000 sprockets.
• The design needs 3 sprockets and 7 widgets
• The company will produce as many units of the new design as the current inventory allows.

To find the values of the new design using 3 sprockets and 7 widgets, it is necessary to find the maximum number of widgets and sprockets. The company would be using these sprockets and widgets from the inventory for producing as many units of the new design.

The condition array states that 1 unit requires 3 sprockets and 7 widgets while the inventory holds 3,500 widgets and 2000 sprockets.

Accordingly, the maximum number of widgets that can be utilized can be equalled to-
3500/7 = 500

The maximum number of sprockets that can be utilized from the inventory can be equalled to –
2000/3 = 666

It can be stated that the least of the two values would supply the maximum number of units that can be made which is hence, equal to 500.
Hence, the total number of widgets that can be used at the maximum can be identified with the fact that 1 unit utilizes only 3 sprockets, which equals 1500 sprockets.

Hence, the number of units produced is 500 and 1500 sprockets are used. 

Approach Solution 2:

The problem statement states that:
Given:

• A manufacturing company is conducting a test to create a new design.
• For the test run, the company currently has an inventory of 3,500 widgets and 2000 sprockets.
• The design requires 3 sprockets and 7 widgets per unit
• The company is ready to make multiple units as much as the current inventory allows.

Find out:

• The value for the number of sprockets used and the value for the number of units produced

Accordingly, the number of units that can be produced can be based on the number of widgets that can be used which is 3500 divided by 7 which gives 500. Hence, the total of units that can be produced with 7 widgets per unit is-
3500/7 which is equal to 500.

The total number of sprockets that are required to produce 1 unit of the design is 3. However, with 500 units that can be produced with 3500 widgets, the total number of sprockets that would be required from the inventory can be found with-

500*number of widgets for each unit
= 500*3 = 1500

Hence, 1500 sprockets would be required to produce 500 units of the new design. 

“A manufacturing company is testing out a new design for one of its most popular products”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. GMAT Problem Solving questions help the candidates to evaluate facts and solve numerical problems. GMAT Quant practice papers enable the candidates to analyse varieties of questions which will help them to improve their mathematical knowledge.

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