Data Sufficiency

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

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