If a club made a gross profit of $0.25 for each candy bar it sold, how

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

target is find total candy bars sold
#1
The total revenue from the sale of the candy bars was $300.
revenue = price * qty
qty and price are not know insufficient
#2If the club had sold 80 more candy bars, its gross profits would have increased by 20 percent.
for 80 more candies the profits increase by 20%
given that gp is .25
so 80*.25 = 20 $ which means that total sale was of 100$
as profits have increased by 20%
actual candies sold ; 100/.25 ; 400
sufficient
OPTION B

One should know that Gross Profit is equal to REVENUE- COST
One can set up the equation 0.25*Q = Net Profit.
So if we know the net profit, we can figure out Q
Fyi: Usually when there are two variables and 1 equation, the answer choice is usually A, B or D (take it with a grain of salt)

1.) Revenue*Q = 300
We don't know the cost value.
Statement 1 is Insufficient

2.) When we convert statement two into a math equation, you get (Q+80)(0.25) = 1.2NP
And we know NP = (0.25)(Q) from the stem
So you get (Q+80)(0.25) = 1.2(0.25)(Q)
Q+80 = 1.2Q
We can solve for Q (no need to actually solve for Q, that would be a waste of time).
STATEMENT 2 is SUFFICIENT

gross profit = revenue - costs

(1) Total revenue = $300

We're told the gross profit is 0.25 for each candy bar; however we don't know the number of candy bars sold. INSUFFICIENT.

(2) If the club had sold 80 more candy bars, its gross profit would have increased by 20 percent.

\(80 * 0.25 = $20\) gross profit (20%)

Therefore 100% gross profit would be $100.

Answer is B.

A: First only statement 1:
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.

The statement tells us nothing about the number of candy bars. It could be 1 bar, 2 bars, ... 150 bars, 300 bars.
Statement 1 is Insufficient

B: Now only statement 2:
If a club made a gross profit of $0.25 for each candy bar it sold, how many candy bars did the club sell?
(2) If the club had sold 80 more candy bars, its gross profits would have increased by 20 percent.

Suppose the club sold n bars.
$0.25 gross profit on each bar, total gross profit = 0.25n

If the club has sold (n+80) bars
Total gross profit would be (0.25)(n+80) = (20% more than the original gross profit) = (1.2)(0.25n)
==> (0.25)(n+80) = (1.2)(0.25n)
==> 0.25n + 20 = 0.3n
==> n can be calculated
Statement 2 is sufficient
The answer is B.

On the dangers of misreading:
This is a fairly straightforward question (despite the 700 tag). It should have been a quick question too, if I hadn't misread Statement 2 as "If the club had sold 80% more candy bars...".
The misreading lead to to the equation 0.45n = 0.3n , reworking my steps, then rereading the statement, and discovering the problem.
On exam day a misreading like this can lead to a wrong answer or waste a LOT of time. Especially because once something is misread, it often stays misread.
The lesson to remember is this: read the text slowly and carefully, with a finger on the screen if necessary.
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