rbakerv wrote:To save money, Arkadelphia Cream Cheese will reduce each dimension of its rectangular box container (which is entirely full of cream cheese) by 50%, and reduce the price it charges its consumers by 50% as well. By what percentage does this increase the price-per-cubic-inch that each consumer will pay for cream cheese?

A) No change
B) 50%
C) 100%
D) 300%
E) 400%

This question is well suited to PLUGGING in nice values.

Let's say that the ORIGINAL dimensions of the box are 2x2x2, which means the volume is 8 cubic inches.
For convenience, let's say the ORIGINAL price is $8.
So, the consumer pays $1 per cubic inch


Now, we'll examine the ALTERED box.
If each side is reduced by 50%, then each side has length 1.
In other words, the dimensions of the ALTERED box are 1x1x1, which means the volume is 1 cubic inch.
If the price of the cheese is reduced by 50%, the NEW PRICE is $4.
So, the consumer pays $4 per cubic inch

The price per cubic inch increases from $1 per cubic inch to $4 per cubic inch, which represents a PERCENT INCREASE of [spoiler]300%[/spoiler]

Answer: D

Cheers,
Brent

Hi rbakerv,

I'm a big fan of TESTing VALUES in these types of questions. That approach puts real numbers in front of you and makes the math really easy to handle. This question can also be solved with Algebra/Geometry though:

We're told that each dimension of a rectangular box will be reduced by 50% - in other words, they will all be cut in HALF. We're also told that the original price of the box will be cut in half.

Since the question does NOT state the dimensions are distinct, we can call each dimension "X"

Original Volume/Price:

Volume = (X)(X)(X)
Price = P

Volume/Price = (X^3)/P

Reduced Volume/Reduced Price

Volume = (X/2)(X/2)(X/2)
Price = (P/2)

Volume/Price = [(X^3)/8]/(P/2)

Now, multiply both the numerator and denominator by 8 (this will remove the fractions in each):

(X^3)/4P

Original Cheese Price = (X^3)/P
New Cheese Price = (X^3)/4P

In real basic terms, we're paying 4 TIMES the price for the same amount of cheese.

The question asks for the PERCENTAGE INCREASE in price/cheese....

Percentage Increase = (New - Old)/Old = (4P - P)/P = 3P/P = 3 = 300%

Final Answer: D

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