Percentage Change

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by [email protected] » Sat Jul 05, 2014 5:03 am

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?

No change

50%

100%

300%

400%

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Source: Beat The GMAT — Problem Solving | Sat Jul 05, 2014 5:03 am

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by [email protected] » Sat Jul 05, 2014 6:08 am

Hi shibsriz,

This question is perfect for TESTing Values:

Let's say that the dimensions of the box are 2in x 2in x 2in, so the Volume is 8 cubic inches. We can also say that the price is $8.

To start, 1 cubic inch = $1

We're told that each dimension will be reduced by 50% AND the price is reduced by 50%.

Now, the dimensions are 1in x 1in x 1in, so the Volume is 1 cubic inch. The price is now $4

Here, 1 cubic inch = $4

The question asks for the percent increase in price per cubic inch, which means we need the Percent Change Formula:

Percent Change = (New - Old)/(Old) = (4 - 1)/1 = 3/1 = 300%

Final Answer: D

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Sat Jul 05, 2014 6:17 am

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?

No change

50%

100%

300%

400%

If the dimensions were L, B and H as Length, Width and Height respectively then the volume of icecream in one box = LxBxH for $a (assumed)
Per unit volume price = (a) / (LxBxH)

Now the new dimensions are L/2, B/2 and H/2 therefore the new amount of Icecream in the box = (L/2)x(B/2)x(H/2) = LxBxH / 8 which she sells for $a/2

Per unit volume price = (a/2) / (LxBxH / 8)

% change = {[(a)/(LxBxH)]-[(a/2)/(LxBxH/8)]}*100 / {(a)/(LxBxH)} = {4-1}*100/1 = 300%

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by GMATGuruNY » Sat Jul 05, 2014 6:42 am

[email protected] 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?

No change

50%

100%

300%

400%

Old box:
Let e = 2 inches.
Volume = eÂ³ = 2Â³ = 8 cubic inches.
Let the total price = $8.
Thus:
Price per cubic inch = (total price)/volume = 8/8 = $1.

New box:
Edge reduced by 50% = 50% of 2 inches = 1 inch.
New volume = 1Â³ = 1 cubic inch.
Price reduced by 50% = 50% of $8 = $4.
Thus:
New price per cubic inch = (new price)/(new volume) = 4/1 = $4.

Many students make SILLY MISTAKES when answering questions about percent change.
To make sure that we choose the correct answer choice, PLUG IN THE ANSWERS.
When the correct percentage is added to the old price per cubic inch -- $1 -- the resulting price must be $4.

Answer choice D: 300%
Adding 300% to $1, we get:
1 + (300/100)(1) = 1+3 = 4.
Success!

The correct answer is D.

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