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by GMATGuruNY » Tue May 24, 2016 7:50 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 [email protected] » Tue May 24, 2016 9:17 am
Hi amina.shaikh309,

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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