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Need to understand a simpler way to solve this OG 13 quest.

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Need to understand a simpler way to solve this OG 13 quest.

by [email protected] » Thu Jul 04, 2013 3:30 am
141. 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 product X were equal to $100,000 plus
5 percent of the company's total revenue from all
units of product X 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.
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Source: — Data Sufficiency |
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by GMATGuruNY » Thu Jul 04, 2013 4:46 am
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.

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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by binit » Fri Apr 24, 2015 11:34 pm
Thanks Mitch for suggesting a wonderful way to solve this. I found that very interesting, yet it would be tough for me to complete in 2 minutes :roll:
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by [email protected] » Sat Apr 25, 2015 10:33 am
Hi shibsriz,

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

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Rich
Last edited by [email protected] on Sun Apr 26, 2015 9:40 am, edited 1 time in total.
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by binit » Sat Apr 25, 2015 9:11 pm
5% of $105,000 = $5,025
$100,000 + $5,025 = $105,025
Hi Rich,
The quoted part may contain calculation errors, otherwise great explanation..

~Binit.
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by [email protected] » Sun Apr 26, 2015 9:44 am
Hi binit,

You are correct; I slipped a digit there. Thanks for the heads-up - I've edited the post accordingly.

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by binit » Fri May 01, 2015 11:16 pm
U r most welcome, Rich.

~Binit.
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