Data Sufficiency

BTGmoderatorDC wrote: ↑

Thu Feb 02, 2023 7:29 pm

If a club made a gross profit of $0.25 for each candy bar it sold, how many candy bars did the club sell?

(1) The total revenue from the sale of the candy bars was $300.
(2) If the club had sold 80 more candy bars, its gross profits would have increased by 20 percent.


OA B

Source: GMAT Prep

Target question: How many candy bars did the club sell?

Given: The club made a gross profit of $0.25 for each candy bar it sold

Statement 1: The total revenue from the sale of the candy bars was $300.
Let x = the wholesale cost of one candy bar (in dollars)
So, x + 0.25 = selling price of one candy bar (in dollars)
Let n = the TOTAL number of candy bars sold

Revenue = (number of candy bars sold)(selling price for a candy bar)
Substitute to get: $300 = (n)(x + 0.25)
As you might imagine, there are many different solutions to this equation.
As such, statement 1 is NOT SUFFICIENT

If you're not convinced, consider these two possible cases:
Case a: The selling price of one candy bar = $300, and the club sold 1 candy bar. In this case, the answer to the target question is the club sold 1 candy bar
Case b: The selling price of one candy bar = $150, and the club sold 2 candy bars. In this case, the answer to the target question is the club sold 2 candy bars
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: If the club had sold 80 more candy bars, its gross profits would have increased by 20 percent.
APPROACH #1
For every candy bar sold, the gross profit increases by $0.25
(80)($0.25) = $20
So, selling 80 more candy bars results in a gross profit increase of $20
If this $20 increase represents a 20% INCREASE in gross profits, then the ACTUAL gross profits must be $100 (since $20 is 20% of $100)
If the ACTUAL gross profits are $100, and since each candy bar sold results in a gross profit increases of $0.25, the total number of candy bars sold = $100/$0.25 = 400
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

APPROACH #2 (faster)
If the sale of 80 more candy bars would have increased profits by 20%, then 80 represents 20% of the total number of candy bars sold.
In other words: 80 = (0.2)(total number of candy bars sold)
Solve to get: total number of candy bars sold = 400
Once again, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent