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To save money, Arkadelphia Cream Cheese will reduce each dimension of

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

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Question Stats:

59% (01:33) correct 41% (01:04) wrong based on 280 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?

1. No change
2. 50%
3. 100%
4. 300%
5. 400%
[Reveal] Spoiler: OA

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

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New post 31 Oct 2014, 12:31
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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New post 31 Oct 2014, 20:27
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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$

Therefore Price / cubic inch = 50 / (20*10*10) = 0.025


Now, when dimensions are reduced by 50% and price also reduced by 50%
L = 10; B=5; H=5 and Price = 25$

Therefore price / cubic inch = 25 / (10*5*5) = 0.1

Percentage change = (0.1 - 0.025) *100/ 0.025 = 3*100 = 300%

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

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New post 06 Feb 2015, 08:33
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.

Calculating the change: [(final - initial) / final] * 100:
[(40-10) / 10] * 100 = (30 / 10) * 100 = 3*100 = 300.

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.

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

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New post 05 Nov 2015, 12:10
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.

So we are paying 4 times extra of current price

(1- 0.25)/ 0.25 = 3

Therefore 300% Ans
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To save money, Arkadelphia Cream Cheese will reduce each dimension of [#permalink]

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New post 09 Nov 2015, 23:33
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%

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

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New post 26 Oct 2016, 12:18
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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%


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%

Answer:
[Reveal] Spoiler:
D


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

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Re: To save money, Arkadelphia Cream Cheese will reduce each dimension of   [#permalink] 17 Nov 2017, 15:39
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