Problem Solving

AAPL wrote:e-GMAT

A seller sold two shoes at the same selling price. If the percentage profit on one of the shoes was 30% and the percentage loss on the other shoe was 30%, find the overall percentage profit or loss made by the seller.

A. 3% loss
B. 3% profit
C. 9% loss
D. 9% profit
E. No profit no loss

OA C.

We see that we will have to deal with a couple of not-so-friendly numbers such as 1/1.3 and 1/0.7. So we must think of a way to get rid of this.

Say the selling price of each shoe = 91 (LCM of 13 and 7)

Thus,

Cost price of the first shoe = 91 / (1 + 30%) = 91 / 1.3 = 910 / 13 = 70
Cost price of the second shoe = 91 / (1 - 30%) = 91 / 0.7 = 910 / 7 = 130

Total cost price = 130 + 70 = 200
Total selling price = 91 + 91 = 182

Since 200 > 182, there is a loss of 18.

Overall loss = (18/200)*100% = 9%

The correct answer: C

Hope this helps!

-Jay
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AAPL wrote:e-GMAT

A seller sold two shoes at the same selling price. If the percentage profit on one of the shoes was 30% and the percentage loss on the other shoe was 30%, find the overall percentage profit or loss made by the seller.

A. 3% loss
B. 3% profit
C. 9% loss
D. 9% profit
E. No profit no loss

We can let the selling price of each shoe = $91. Thus, for the shoe that has 30% profit, the purchasing cost, x, can be determined by the equation:

x(1.3) = 91

x = 91/1.3 = 70

Likewise, for the shoe that has 30% loss, the purchasing cost, y, can be determined by the equation:

y(0.7) = 91

x = 91/0.7 = 130

Therefore, the total cost of the two shoes is 70 + 130 = $200 and the total revenue of the two shoes is 2(91) = $182. Therefore, the percent change is (182 - 200)/200 = -18/200 = -9%, i.e., the seller has a 9% loss.

Answer: C

Hi All,

We're told that a seller sold two shoes at the SAME selling price; the percentage profit on one of the shoes was 30% and the percentage loss on the other shoe was 30%. We're asked for the overall percentage profit or loss made by the seller. This question can be solved by TESTing VALUES - and the answer choices are sufficiently 'spread out' that we don't have to worry about trying to find the 'perfect' numbers to TEST: the number 100 will be fine.

To start, we have to create two equations to figure out the individual profit and loss described (we can set the selling price for each shoe at $100):

The shoe that was sold for a 30% profit:
X + .3X = $100
1.3X = $100
X = 100/1.3 = 1000/13 = about $77 --> this is a PROFIT of $100 - $77 = $23

The shoe that was sold for a 30% loss:
Y - .3Y = $100
.7Y = $100
Y = 100/.7 = 1000/7 = about $143 --> this is a LOSS of $143 - $100 = $43

Thus, the 'net' of the two sales is $23 - $43 = - $20 --> a LOSS of about $20

Since the total sale price of the two shoes is $100 + $100 = $200, we know that $20 is 10%, so the LOSS was about a 10% loss. There's only one answer that makes sense...

Final Answer: C

GMAT assassins aren't born, they're made,
Rich