I15-04

Question

The table below provides details of the revenue and expenses (in USD) incurred by six companies (A to F) over a three-year period: 2011, 2012, and 2013. Profit or loss is calculated as Revenue - Expenses.
      Year   Year 2011   Year 2012   Year 2013       Company   Revenue   Expenses   Revenue   Expenses   Revenue   Expenses       A   50,000   40,000   75,000   60,000   60,000   80,000       B   60,000   50,000   70,000   70,000   100,000   80,000       C   45,000   35,000   60,000   65,000   85,000   80,000       D   50,000   40,000   70,000   60,000   70,000   80,000       E   45,000   40,000   65,000   60,000   80,000   85,000       F   40,000   20,000   50,000   60,000   90,000   50,000

For each of the following statements, select  Yes  if the statement is true based on the information provided. Otherwise, select  No .

Bunuel · Answer

Official Solution:

Statement 1: 
 
To evaluate this statement, we need to compare revenue and expenses for each company over the three-year period. Upon review, we can see that Company B did not incur a loss in any of the years—it broke even in 2012 and made a profit in both 2011 and 2013. Therefore, this statement is not true.
 
 Statement 2: 
 
The highest profit as a percentage of expenses essentially means the highest revenue-to-expenses ratio. The highest ratio in 2013 was for Company F: 90,000/50,000 = 1.8 (80% profit). Let's check if any company in 2011 or 2012 had a higher revenue-to-expenses ratio. Quickly scanning the data, we can see that in 2011, Company F had an even higher ratio: 40,000/20,000 = 2, indicating a profit of 100%. Therefore, this statement is not true.
 
 Statement 3: 
 
Companies A, C, D, E, and F experienced a loss in at least one year, while Company B broke even in 2012, meaning it did not incur a profit either. Therefore, this statement is true.

Correct answer:

Each company incurred a loss in at least one of the three years.  "No"

The highest profit as a percentage of expenses incurred by any company was in 2013.  "No"

Each company did not incur a profit for at least one of the three years.  "Yes"

Bunuel · Answer

I have revised the question, solution, and formatting by adding more details to enhance clarity.

godinero · Answer

I like the solution - it’s helpful.

Nishith27 · Answer

I did not quite understand the solution. The highest profit as a percentage of expenses incurred by any company should be calculated as 'profit/expense' instead of revenue-to-expenses ratio.

Bunuel · Answer

Profit as a percentage of expenses is:

profit/expenses = (revenue - expenses)/expenses = revenue/expenses - 1

So comparing profit/expenses is exactly the same as comparing revenue/expenses. Whoever has the highest revenue/expenses also has the highest profit/expenses. That is why the solution uses the revenue-to-expenses ratio, because it produces the same ranking and is simpler to calculate.

I15-04

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Company	Revenue	Expenses	Revenue	Expenses	Revenue	Expenses
Year	Year 2011		Year 2012		Year 2013
A	50,000	40,000	75,000	60,000	60,000	80,000
B	60,000	50,000	70,000	70,000	100,000	80,000
C	45,000	35,000	60,000	65,000	85,000	80,000
D	50,000	40,000	70,000	60,000	70,000	80,000
E	45,000	40,000	65,000	60,000	80,000	85,000
F	40,000	20,000	50,000	60,000	90,000	50,000