A factory has a fixed cost of $45,000 a month, and a cost

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

A factory has a fixed cost of $45,000 a month, and a cost

by VJesus12 » Sat Jan 27, 2018 8:15 am

A factory has a fixed cost of $45,000 a month, and a cost of $2.5 for every item produced. If the selling price of a single item is $5, what is the number of items must be sold monthly for the factory to cover its cost exactly?

A. 9,000
B. 14,000
C. 18,000
D. 22,500
E. 27,000

The OA is the option C.

Why is not the option A correct? I am confused here. Experts, can you help me? Thanks.

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Source: Beat The GMAT — Problem Solving | Sat Jan 27, 2018 8:15 am

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

by EconomistGMATTutor » Sat Jan 27, 2018 8:59 am

Hello vjesus12.

Let's see your question.

The fixed cost is $45,000.

The cost of each item is $2.5.

The price of each item is $5.

So, when an item is sold the profit is $5-$2.5 = $2.5.

Now, we have to divide the fixed cost by the profit for each item, that is to say, $$\frac{45,000}{2.5}=18,000\ \text{dollars}.$$ This is why the correct answer is the option C .

I hope this answer can help you.

If you have a doubt, I can help you.

Regards.

GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Sat Jan 27, 2018 11:06 am

Hi VJesus12,

We're told that a factory has a fixed cost of $45,000 a month, a cost of $2.50 for every item produced and a selling price of a single item is $5. We're asked for the number of items that must be sold each month for the factory to cover its costs exactly. This question can be solved in a couple of different ways, depending on how you choose to do the math. Here's how you can use a little math - and some estimation (along with the 'spread' of the answer choices) - to get to the correct answer.

To start, each item sold has a profit of $5 - $2.50 = $2.50

Selling 10,000 items would get you a profit of... ($2.50)(10,000) = $25,000
Selling 20,000 items would get you a profit of... ($2.50)(20,000) = $50,000

We need to cover the fixed cost of $45,000, so the number of items sold has to be LESS than 20,000... but closer to 20,000 than it is to 10,000. There's only one answer that matches....

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sun Jul 28, 2019 8:37 am

VJesus12 wrote:A factory has a fixed cost of $45,000 a month, and a cost of $2.5 for every item produced. If the selling price of a single item is $5, what is the number of items must be sold monthly for the factory to cover its cost exactly?

A. 9,000
B. 14,000
C. 18,000
D. 22,500
E. 27,000

The OA is the option C.

Why is not the option A correct? I am confused here. Experts, can you help me? Thanks.

We can create the equation:

45,000 + 2.5n = 5n

45,000 = 2.5n

18,000 = n

Alternate Solution:

The company makes a profit of 5 - 2.5 = $2.5 per item. Therefore, to cover the cost of $45,000; the company must sell 45000/2.5 = 18,000 items.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]