A certain company (OG13)

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alex.gellatly: Master | Next Rank: 500 Posts; Posts: 435; Joined: Wed Nov 16, 2011 7:27 am; Thanked: 48 times; Followed by:16 members

A certain company (OG13)

by alex.gellatly » Thu Aug 02, 2012 11:23 pm

Last year, a certain company began manufacturing product X and sold every unit of product X that it produced. Last year the company's total expenses for manufacturing productXwere equal to $100,000 plus 5 percent of the company's total revenue from all units of productX sold. If the company made a profit on product X last year, did the company sell more than 21,000 units of product X last year?
(1) The company's total revenue from the sale of product X last yearwas greaterthan $110,000.
(2) For each unitof productX sold last year, the company's revenue was $5.

Thanks

A useful website I found that has every quant OG video explanation:

https://www.beatthegmat.com/useful-websi ... tml#475231

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Source: Beat The GMAT — Data Sufficiency | Thu Aug 02, 2012 11:23 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Fri Aug 03, 2012 2:42 am

alex.gellatly wrote:Last year, a certain company began manufacturing product X and sold every unit of product X that it produced. Last year the company's total expenses for manufacturing productXwere equal to $100,000 plus 5 percent of the company's total revenue from all units of productX sold. If the company made a profit on product X last year, did the company sell more than 21,000 units of product X last year?
(1) The company's total revenue from the sale of product X last year was greater than $110,000.
(2) For each unit of product X sold last year, the company's revenue was $5.

Thanks

Statement 1: The company's total revenue from the sale of product X last year was greater than $110,000.
No way to determine the number of units sold.
INSUFFICIENT.

Statement 2: For each unit of product X sold last year, the company's revenue was $5.
Plug in the THRESHOLD of 21,000 units:
Total revenue = 5(21,000) = 105,000.
Total expenses = 100,000 + .05(105,000) = 105,250.
Not possible, since the company must make a profit.
Test a GREATER number of units: 100,000.
Total revenue = 5(100,000) = 500,000.
Total expenses = 100,000 + .05(500,000) = 125,000.
Here, the company makes a profit.
Thus, to make a profit, the company must sell MORE than 21,000 units.
SUFFICIENT.

The correct answer is B.

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Nina1987: Senior | Next Rank: 100 Posts; Posts: 79; Joined: Tue Dec 15, 2015 3:56 am; Followed by:1 members; GMAT Score:750

by Nina1987 » Thu Feb 11, 2016 11:56 pm

So the first thing that jumps at you is it's a break-even analysis problem. So the question is gonna test us no of units for break even somewhere.

What is asked is x>21,000?
What should be x at the break-even,
100,000+p(.05)=xp ..where p is per unit selling price.
--> x = 100,000/0.95p
So, the question becomes, 100,000/0.95p>21,000?

Note that we will need only p to be able to answer the question. So, St2 looks easier lets take a look at it.
St2: 100,000/.95*5>21,000?
400/19>21?
400>21*19? We know this is true as 21*19 will always be less than 20*20=400( PS: 9*11<10*10, 4*6<5*5 etc I think you get the idea)
SUFF

St1: clearly insufficient it could be just 1 heavy m/c or 110,000 widgets sold.

Ans B

If you want to save some more time then the moment you suspect a break-even problem you should think of the following the formula: : No of Units= Total Fixed Cost/Per Unit Profit. Most of the GMAT problem on this topic will play around this formula. Another formula to remember is
No of Units=Gross Profit/Per Unit Profit
For break even analysis pls check - https://en.wikipedia.org/wiki/Break-even_(economics)

Last edited by Nina1987 on Sat Feb 13, 2016 7:25 am, edited 1 time in total.

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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] » Fri Feb 12, 2016 10:21 am

Hi All,

GMAT questions are always carefully worded - the numbers involved are NEVER random and the questions asked are specifically-worded for a reason. As such, you can take advantage of those patterns when working through Quant questions.

Here, we're told a number of facts about a company:
1) It sold EVERY unit of product X that it produced.
2) Total expenses were $100,000 + 5% of revenue from those sales.
3) The company made a PROFIT on these sales.

The question asks if the company sold MORE than 21,000 units of product X. This is a YES/NO question.

Before dealing with the two Facts, notice that the expenses were MORE than $100,000 (since the revenue factors in to that calculation), but we know that the company made a PROFIT. That combination of facts will come in handy in just a moment....

Fact 1: Total revenue from product X was GREATER than $110,000

This confirms something that we already knew (the company made a profit), but we don't know how many units were sold to earn that revenue.
Fact 1 is INSUFFICIENT

Fact 2: Each unit of Product X sold brought in $5 of revenue.

Since the question asks specifically if MORE than 21,000 units were sold, we can use this number as a 'gauge'....

IF....
21,000 units were sold at $5 per unit, we'd have 21,000(5) = $105,000 of revenue

We were told that the EXPENSES = $100,000 + 5% of revenue.....

5% of $105,000 = $5,250
$100,000 + $5,250 = $105,250
In this scenario, the expenses are GREATER than the revenue....
BUT we were told that the company made a PROFIT, so this CANNOT be what happened. If only 21,000 units were sold at this price, then the company would NOT have been profitable. Thus, MORE than 21,000 units would have to have been sold.
Fact 2 is SUFFICIENT

Final Answer: B

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

Contact Rich at [email protected]

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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

Re: A certain company (OG13)

by Scott@TargetTestPrep » Thu May 20, 2021 9:14 am

alex.gellatly wrote: ↑
Thu Aug 02, 2012 11:23 pm
Last year, a certain company began manufacturing product X and sold every unit of product X that it produced. Last year the company's total expenses for manufacturing productXwere equal to $100,000 plus 5 percent of the company's total revenue from all units of productX sold. If the company made a profit on product X last year, did the company sell more than 21,000 units of product X last year?
(1) The company's total revenue from the sale of product X last yearwas greaterthan $110,000.
(2) For each unitof productX sold last year, the company's revenue was $5.

Thanks

Solution:

Question Stem Analysis:

We need to determine whether the company sold more than 21,000 units of product X last year.

Statement One Alone:

We are given that the company's total revenue from the sale of product X last year was greater than $110,000. We have a lower bound for the total revenue and we can calculate a lower bound for the total cost, but we have no information from which we can determine a lower bound for the number of units. It is possible that the company sold 25,000 units and made a revenue of $150,000 (in which case, the total cost would be 100,000 + 0.05(150,000) = $107,500), and it is possible that the company sold 20,000 units and made the same revenue. We see that the company makes a profit on product X in either case. Statement one alone is not sufficient.

Statement Two Alone:

Let the number of product X sold by the company last year be n. Since each unit generates a revenue of $5, the total revenue is 5n. We are told that the total cost is 5 percent of 5n plus $100,000; therefore the cost can be represented as 100,000 + 0.05(5n) = 100,000 + 0.25n. We are also told that the company made a profit from the sale of product X, therefore the revenue is greater than the cost. Using this information, we can create the following inequality:

5n > 100,000 + 0.25n

4.75n > 100,000

n > 100,000/4.75 ≈ 21,053

We see that n, the number of units of product X sold, is greater than 21,000. Statement two alone is sufficient.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]