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A store purchased 20 coats that each cost an equal amount

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A store purchased 20 coats that each cost an equal amount

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A store purchased 20 coats that each cost an equal amount and then sold each of the 20 coats at an equal price. What was the store’s gross profit on 20 coats?

(1) If the selling price per coat had been twice as much , the store’s gross profit on the 20 coats would have been $2,400

(2) If the selling price per coat had been $2 more, the store’s gross profit on the 20 coats would have been $440

OA B

Source: GMAT Prep

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BTGmoderatorDC wrote:
A store purchased 20 coats that each cost an equal amount and then sold each of the 20 coats at an equal price. What was the store’s gross profit on 20 coats?

(1) If the selling price per coat had been twice as much , the store’s gross profit on the 20 coats would have been $2,400

(2) If the selling price per coat had been $2 more, the store’s gross profit on the 20 coats would have been $440
Statement 1: If the selling price per coat had been twice as much , the store’s gross profit on the 20 coats would have been $2,400
When the selling price per coat is doubled, the resulting profit per coat = (total profit)/(number of coats) = 2400/20 = 120.

Case 1: Double the selling price = 130, implying that the cost per coat = 130-120 = 10 and that the actual selling price = 130/2 = 65
In this case, the actual profit per coat = (actual selling price) - (cost) = 65-10 = 55

Case 2: Double the selling price = 140, implying that the cost per coat 140-120 = 20 and that the actual selling price = 140/2 = 70
In this case, the actual profit per coat = (actual selling price) - (cost) = 70-20 = 50

Since the profit per coat can be different values, INSUFFICIENT.

Statement 2: If the selling price per coat had been $2 more, the store’s gross profit on the 20 coats would have been $440
When the selling price is increased by $2, the resulting profit per coat = (total profit)/(number of coats) = 440/20 = 22.
Since the actual selling price is $2 less, the actual profit per coat = 22-2 = 20.
Since each of the 20 coats yields an actual profit of $20, the total gross profit for all 20 coats = 20*20 = 400.
SUFFICIENT.

The correct answer is B.

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BTGmoderatorDC wrote:
A store purchased 20 coats that each cost an equal amount and then sold each of the 20 coats at an equal price. What was the store’s gross profit on 20 coats?

(1) If the selling price per coat had been twice as much , the store’s gross profit on the 20 coats would have been $2,400

(2) If the selling price per coat had been $2 more, the store’s gross profit on the 20 coats would have been $440

OA B

Source: GMAT Prep
Say the selling price of each coat is %y and the cost price is $x.

Thus, gross profit on 20 coats = 20(y - x).

We have to get the value of (y - x).

Let's take each statement one by one.

(1) If the selling price per coat had been twice as much, the store’s gross profit on the 20 coats would have been $2,400.

=> 20(2y - x) = 2400

2y - x = 120

Can't get the value of (y - x). Insufficient.

(2) If the selling price per coat had been $2 more, the store’s gross profit on the 20 coats would have been $440.

=> 20[(y +2) - x] = 440

(y +2) - x = 22

y - x = 20

Thus, gross profit on 20 coats = 20(y - x) = 20*20 = $400. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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