A store purchased 20 coats that each cost

[alysekilleen]

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 the 20 coats?

1) If the selling price of the 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 would have been $440.

This is a data sufficiency problem and the correct answer is b.

I am having a hard time reconciling the two statements (which seem to be conflicting).

Please explain so that I can understand the technique and how to apply it to another similar DS question (ie. what exactly does statement 2 have that statement 1 doesn't).

Thank you!

[james.jt.wu]

Hi there :)

Let me take a crack at this question for you. Two key principles to this question:

1.) Understand that profit = Sales Price * Quantity - Bought Price * Quantity
2.) Look for algebraic "combos."
3.) Always try to rephrase the stem as much as you can before going into the choices.

Let's rephrase the question stem.

X = bought price
Y = sales price
20 coats total bought and sold

So the profit's equation becomes:

Sale Price * Quantity - Bought Price * Quantity = 20Y - 20X, which can be simplified to

20(Y-X).

Therefore, the rephrase of the stem is: What is Y-X????.

Note that you DO NOT need the individual valus of Y and X to answer the question, just the combo of Y-X.

Let's now go to the stem:

Statement 1

This says that if the selling price (Y) doubles, the gross profit would have been 2,400. So that means at the selling price of 2Y, the profit would have been 2,400. Let's translate this into algebra to see if we can get a value for Y-X.

The total new profit is 20(2Y) - 20(X) = 2,400. X is the bought price and that didn't change.

This simplifies to 2Y-X = 120. as you can see, we can't isolate Y-X by itself on one side. There isn't an equation given by the stem either, so you can't solve for Y and X individually. Therefore, Statement 1 is insufficient.

Statement 2

We do the exact same exercise here, let's see what happens with the algebra.

20(Y+2) - 20X = 440.
20Y+40 - 20X = 440
20Y - 20X = 400
20(Y-X) = 400
(Y-X) = 20.

Sufficient! You got Y-X by itself with a specified value. Therefore the answer is B.

To answer your question on whether these two statements are conflicting - they're not! GMAT will never give you statements that give you conflicting answers (a statement may show more than the other statement, but they would never give you contradictory info.)

To see this, all you have to do is solve the system equation of the equations from Statement 1 and 2, and you will give an unique value that satisfies both Statement 1 and 2.

Hope this helps!

James

[RonPurewal]

james, solid analysis.

as for the second statement, if you have enough of an intuitive understanding of gross profit, you can simplify the consideration of that statement.
specifically:

gross profit is
(TOTAL REVENUE) - (TOTAL COST)
if you sell the coats for an additional two dollars each, then you are just adding $40 to your total revenue (since we know that a total of 20 coats are sold).
therefore,
we are being GIVEN a value for
(TOTAL REVENUE + 40) - (TOTAL COST)
this is just 40 greater than the desired value, so you can find the desired value by just subtracting 40.
sufficient.