Bunuel
What was a certain company's revenue last year?
(1) Last year gross profit was $4,100
(2) Last year revenue was 50% greater than expenses
Target question: What was a certain company's revenue last year?Key concept: revenue - expenses = profit Statement 1: Last year gross profit was $4,100 Since we have no information about the expenses, there is no way we can answer the target question.
Statement 1 is NOT SUFFICIENT
If you're not convinced consider these two possible cases that satisfy statement 1:
Case a: expenses = $1000 and profit = $4100. Since
revenue - expenses = profit, we can write:
revenue - $1000 = $4100, which means
revenue = $5100Case b: expenses = $2000 and profit = $4100. Since
revenue - expenses = profit, we can write:
revenue - $2000 = $4100, which means
revenue = $6100Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: Last year revenue was 50% greater than expensesThere are many scenarios that satisfy statement 2. Here are two:
Case a: expenses = $100 and revenue = $150 (notice that revenue is 50% greater than expenses). In this case, the answer to the target question is
revenue = $150Case b: expenses = $10 and revenue = $15 (notice that revenue is 50% greater than expenses). In this case, the answer to the target question is
revenue = $15Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 2 tells us that revenue was 50% greater than expenses. So, if we let
x = expenses, then
1.5x = revenueStatement 1 tells us that
profit = $4,100Since
revenue - expenses = profit, we can write:
1.5x - x = $4100At this point, we COULD solve this equation for x, which means we COULD answer the target question with certainty (of course, on test day, he would never waste our time solving the equation, since we need only determine whether or not we have sufficient information to answer to Target question)
For "fun" let's solve the equation
1.5x - x = $4100Simplify the left side to get: 0.5x = $4100
Divide both sides by 0.5 to get: x = $8200
Since
1.5x = revenue, we know that the
revenue = 1.5($8200) = $12,300Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent