Problem Solving

[email protected] wrote:Hi lheiannie07,

While this question involves a lot of information to keep track of, we can ultimately solve it by TESTing VALUES (albeit in a slightly "out-of-order" way).

To start, we have no idea what the original price of the laptops were and we don't know what the 'marked up' prices were. I'm going to start with the MARKED UP price and come back to the original price later on:

Marked Up Price = $1,000

Ally sold her laptop after giving a $200 discount, THEN a 20% off discount:
$1,000 - $200 = $800
$800 - (20% of $800) = $800 - $160 = $640

Tom sold his laptop after giving a 20% discount, THEN a $200 off discount:
$1,000 - (20% of $1000) = $1000 - $200 = $800
$800 - $200 = $600

We're told that Ally made a PROFIT that was EQUAL to Tom's LOSS. With sell prices of $640 and $600, respectively, the original purchase price would have had to have been $620

Ally = $640 - $620 = $20 profit
Tom = $600 - $620 = $20 loss

Thus, Ally's profit = $20

Final Answer: A

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

GMATGuruNY wrote:

lheiannie07 wrote:Tom and Aly purchased a laptop each at the same price. Both of them marked up the price of their laptops by the same amount. Aly sold her laptop by offering successive discounts of $200 and 20%, in that order; whereas Tom sold his laptop by offering the same scheme of discount but in reverse order. If the profit made by Aly was equal to the loss incurred by Tom, then what was the amount of profit (in $) made by Aly?
(A) $20
(B) $25
(C) $30
(D) $35
(E) $40

Let the original selling price of each laptop = 500.

Aly sold her laptop by offering successive discounts of $200 and 20%, in that order.
After applying a $200 discount, we get:
500-200 = 300.
After applying a 20% discount, we get:
300 - (20% of 300) = 300 - 60 = 240.

Tom sold his laptop by offering the same scheme of discount but in reverse order.
After applying a 20% discount, we get:
500 - (20% of 500) = 500 - 100 = 400.
After applying a $200 discount, we get:
400-200 = 200.

The profit made by Aly was equal to the loss incurred by Tom
Let C = the cost price of each laptop.
Aly's profit = (Aly's selling price) - (cost price) = 240-C.
Tom's loss = (cost price) - (Tom's selling price) = C-200.
Since Aly's profit and Tom's loss are equal, we get:
240-C = C-200
440 = 2C
220 = C.

What was the amount of profit made by Aly?
Aly's profit = (Aly's selling price) - (cost price) = 240-220 = 20.

The correct answer is A.

[email protected] wrote:Hi lheiannie07,

You could certainly solve this question Algebraically, but there might be a point at which you don't know what to do next.... Let's call the sell price of each laptop X:

Aly: a $200 discount, then a 20% discount would give us....
(X - 200)(.8) = .8X - 160

Tom: a 20% discount, then a $200 discount would give us...
.8X - 200

When you compare the two prices, you'll notice that they are remarkably similar:
Aly = .8X - $160
Tom = .8X - $200

The difference in those two values is $40. From here, the last 'step' is to recognize that Aly's PROFIT is the SAME as Tom's LOSS, so that $40 difference would be a $20 profit for Aly and a $20 loss for Tom

Final Answer: A

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