Please provide a detailed solution for this problem

[Architj]

In 2010, a certain company started the manufacture of product P. The company sold all the units of P manufactured by it in 2010 in that year itself at $7.50 per unit. the total expenses of the company for manufacturing P in 2010 was equal to $150,000 plus 4 percent of its total revenue in selling units of P in 2010. Did the company sell more than 20,830 units of P in 2010?

I. the company did not make a loss on P in 2010.
II. the company did not make a profit on P in 2010.

[GMATGuruNY]

The problem below is virtually the same as the following problem in the OG13:
https://www.beatthegmat.com/need-to-unde ... 65811.html

In 2010, a certain company started the manufacture of product P. The company sold all the units of P manufactured by it in 2010 in that year itself at $7.50 per unit. the total expenses of the company for manufacturing P in 2010 was equal to $150,000 plus 4 percent of its total revenue in selling units of P in 2010. Did the company sell more than 20,830 units of P in 2010?

I. the company did not make a loss on P in 2010.
II. the company did not make a profit on P in 2010.

Let x = the number of units sold.
Since each unit is sold for $7.50, total revenue = 7.5x.
Total expenses = 150,000 + 4% of total revenue = 150,000 + (0.04)(7.5x).

To make a profit, total revenue must exceed total expenses:
7.5x > 150,000 + (0.04)(7.5x)
7.5x > 150,000 + 0.3x
7.2x > 150,000
x > 20,833.33.

Since the number of units sold must be an INTEGER VALUE, the resulting inequality implies the following:
If x≥20,834, the company makes a profit.
If x≤20,833, the company suffers a loss.

Statement 1:
Since the company did not suffer a loss, x≥20,834.
Thus, more than 20,830 units were sold.
SUFFICIENT.

Statement 2:
Since the company did not make a profit, x≤20,833.
If x=20,833, then more than 20,830 units were sold.
If x=20,000, then fewer than 20,830 units were sold.
INSUFFICIENT.

The correct answer is A,

[binit]

Hi GMATGuruNY,

To me, this question was pretty wordy and involved lot of calculations. It took me hell lot of time and I ended up doing a careless mistake too :roll: Would you pls. suggest the level of the Qns of this sort?