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To save money, Arkadelphia Cream Cheese will reduce each dimension of [#permalink]

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31 Oct 2014, 13:30

2

4

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

58% (01:26) correct 42% (01:09) wrong based on 375 sessions

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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?

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Re: To save money, Arkadelphia Cream Cheese will reduce each dimension of [#permalink]

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31 Oct 2014, 21:27

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JusTLucK04 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?

1. No change 2. 50% 3. 100% 4. 300% 5. 400%

Answer is D

Explanation:

Take smart numbers Let, L = 20: B = 10: H= 10 of initial box and Price = 50$

Re: To save money, Arkadelphia Cream Cheese will reduce each dimension of [#permalink]

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31 Oct 2014, 13:31

1

If the current volume is L * W * H, then the new volume is 12 (L) * 12 (W) * 12 (H), or 18 * LWH. So the new portion is 1/8 the size of the old portion. But the new cost is only ½ the cost, meaning that if the old price-per-unit was 1:1, now it’s 12 : 18, or 4:1. So the consumer is paying 400% of what it used to, or 300% more than it used to. The answer is therefore D.
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Re: To save money, Arkadelphia Cream Cheese will reduce each dimension of [#permalink]

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06 Feb 2015, 09:33

Thank you. I picked numbers to do it, like this:

L*W*H are the dimesnions of the container. I chose 1*2*2 respectively, for each dimension.

The container initially had a capacity of 1*2*2 = 4. Lets give it a price of 40. Then per cubic inch it would be 40/4 = 10.

The container was then reduced in half, so it became: 1/2*2/2*2/2 = 1/2. The price was reduced in half, so it became 20. Then per cubic inch it would be 20 / (1/2) = 40.

Now, I find that there are 2 tricky parts: 1) By what percentage does this increase the price-per-cubic-inch that each consumer will pay for cream cheese? 2) There are 3 dimensions. So, if you assume that the box at first had a capacity of 10, which was then reduced into 5, you would have got it wrong.

To save money, Arkadelphia Cream Cheese will reduce each dimension of [#permalink]

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05 Nov 2015, 13:10

1

Let Current L:B:H= 2:2:2 => Current Volume = 2x2x2 = 8

New Dimension = 1:1:1 New Volume = 1x1x1 = 1

Let Current Price is 2 bugs. So, new price will be 1 bug

So now we can say in current scenario we are paying 2 bugs for 8 candies OR 1 bug for 4 candies Or 0.25 bug for 1 candy But now we are paying 1 bug for 1 candy.

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To save money, Arkadelphia Cream Cheese will reduce each dimension of [#permalink]

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10 Nov 2015, 00:33

New volume will be 1/2*1/2*1/2 or 1/8 of old New Price …………………………………1/2 of old Let, volume…………price…………price per unit Old : 8…………….. 8……………… 1 New: 1………………4………………..4 Increase= (4-1)/1*100%=300%

Re: To save money, Arkadelphia Cream Cheese will reduce each dimension of [#permalink]

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26 Oct 2016, 13:18

1

Top Contributor

JusTLucK04 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?

1. No change 2. 50% 3. 100% 4. 300% 5. 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 300%

Re: To save money, Arkadelphia Cream Cheese will reduce each dimension of [#permalink]

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25 Feb 2018, 16:09

Hi All,

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....