The table below provides details of the revenue and expenses (in USD)

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 · Accepted 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"

Bismuth83 · Answer

1. We have to  check whether the following statements are true or false .

2.  Each company incurred a loss in at least one of the three years.  A loss happens when Revenue - Expenses < 0. For all companies except B we can that this is true. As for company B we have the following:

- Year 2011. 60000 - 50000 = 10000 > 0.
 - Year 2012. 70000 - 70000 = 0 = 0.
 - Year 2013. 100000 - 80000 = 20000 > 0.

No losses happen.   So, this statement is false.

3.  The highest profit as a percentage of expenses incurred by any company was in 2013.  Company F in 2011 had 2 times more profit than expenses (200%). However no company in 2013 and anything near that.   So, this statement is false.

4.  Each company did not incur a profit for at least one of the three years.  This is similar to the first statement. All companies except B had losses, which is also not incurring a profit. Looking at company B year 2012, the difference is 0, which means that they also didn't incur a loss.   So, this statement is true.

sbyongid · Answer

i have trouble understanding the expression " highest profit as a percentage of expenses" 
shouldnt it be profit/expense? why is it revenue-expense ratio

Bismuth83 · Answer

You're correct that we're comparing  \frac{Profit}{Expenses} . However, we can simplify as  \frac{Profit}{Expenses} = \frac{Revenue - Expenses}{Expenses} = \frac{Revenue}{Expenses} - 1 , which is the same as comparing just the ratio between revenue and expenses.

I hope that helped!

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The table below provides details of the revenue and expenses (in USD)

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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

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The table below provides details of the revenue and expenses (in USD)

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