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Senior Manager  B
Joined: 17 Sep 2013
Posts: 329
Concentration: Strategy, General Management
GMAT 1: 730 Q51 V38 WE: Analyst (Consulting)
To save money, Arkadelphia Cream Cheese will reduce each dimension of  [#permalink]

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10 00:00

Difficulty:   65% (hard)

Question Stats: 62% (01:58) correct 38% (02:14) wrong based on 510 sessions

### HideShow timer Statistics 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%

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

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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%

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

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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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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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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.

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 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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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%

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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: To save money, Arkadelphia Cream Cheese will reduce each dimension of  [#permalink]

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1
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....

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

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Manager  B
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Location: India
To save money, Arkadelphia Cream Cheese will reduce each dimension of  [#permalink]

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Hi All,

In such questions where we pick numbers, is there a general strategy that we should keep in mind?

I am not able to follow any of the explanations above, for instance, the first explanation in this post takes L=20 and W=10 and H=10 ( no idea, how that is taken)

Would appreciate any help on this.

Also I tried the question in this way and go the incorrect answer

Old Volume= LWH Old Price= P -> Volume/Price=LWH/P
New Volume= LWH(1-50/100)= LWH/2 New Price=P/2 -> Volume Price=LWH/P

Where am I going wrong Adding the experts if they can help with this- Bunuel, chetan2u

Thanks,

Originally posted by Amirfunc on 04 Aug 2018, 08:50.
Last edited by Amirfunc on 04 Aug 2018, 18:52, edited 1 time in total.
Manager  B
Joined: 12 Mar 2018
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GMAT 1: 630 Q49 V27 GPA: 4
To save money, Arkadelphia Cream Cheese will reduce each dimension of  [#permalink]

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Too much hungama!
Though I answered wrongly because I read the question too fast and took only the length and the breadth into account (since it was mentioned rectangular box) I imagined it in 2D. After answering I realized it was in 3D.

Lets assume L =10, B=10, H=10.
and cost per cubic inch = 1 unit(dollar or inr or anything).
so total cost before change = 1000 Dollars. (10*10*10*1).
and total cost after change = 500 Dollars but this is paid for 125 cubic metres. (since we lost 50% in each of the dimension l,b,h 0.5l*0.5b*0.5h = 5*5*5). so total cost per cubic inch is 4 dollars.
(500/125 = 4)

It was 1 dollar now it became 4 dollars. Thus 300% increase.
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Re: To save money, Arkadelphia Cream Cheese will reduce each dimension of  [#permalink]

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Amirfunc wrote:
Hi All,

In such questions where we pick numbers, is there a general strategy that we should keep in mind?

I am not able to follow any of the explanations above, for instance, the first explanation in this post takes L=20 and W=10 and H=10 ( no idea, how that is taken)

Would appreciate any help on this.

Also I tried the question in this way and go the incorrect answer

Old Volume= LWH Old Price= P -> Volume/Price=LWH/P
New Volume= LWH(1-50/100)= LWH/2 New Price=P/2 -> Volume Price=LWH/P

Where am I going wrong Adding the experts if they can help with this- Bunuel, chetan2u

Thanks,

point wise replies...
1) Strategy for choosing number
you should choose number that can make your calculations easier..
here you are reducing each of teh dimensions by 50% or 1/2, so choose even numbers so that each after halfing is a integer..
had it been 1/3, you should have taken multiple of 3...
and choose number that ease your calculation, so 10*10*10 will be better than 24*12*12
2)
Quote:
Old Volume= LWH Old Price= P -> Volume/Price=LWH/P
New Volume= LWH(1-50/100)= LWH/2 New Price=P/2 -> Volume Price=LWH/P

where you hav egone wrong is that we are doing 50% of EACH dimension and not the VOLUME..
New Volume= LWH(1-50/100)(1-50/100)(1-50/100)= LWH/8 New Price=P/2 -> Volume Price=(LWH/8)/(P/2)=2LWH/8P=lwh/4p
lwh/4p is 4 times of lwh/p so extra paid is 4-1 = 3 times and hence 300%..
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Re: To save money, Arkadelphia Cream Cheese will reduce each dimension of  [#permalink]

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chetan2u wrote:
Amirfunc wrote:
Hi All,

In such questions where we pick numbers, is there a general strategy that we should keep in mind?

I am not able to follow any of the explanations above, for instance, the first explanation in this post takes L=20 and W=10 and H=10 ( no idea, how that is taken)

Would appreciate any help on this.

Also I tried the question in this way and go the incorrect answer

Old Volume= LWH Old Price= P -> Volume/Price=LWH/P
New Volume= LWH(1-50/100)= LWH/2 New Price=P/2 -> Volume Price=LWH/P

Where am I going wrong Adding the experts if they can help with this- Bunuel, chetan2u

Thanks,

point wise replies...
1) Strategy for choosing number
you should choose number that can make your calculations easier..
here you are reducing each of teh dimensions by 50% or 1/2, so choose even numbers so that each after halfing is a integer..
had it been 1/3, you should have taken multiple of 3...
and choose number that ease your calculation, so 10*10*10 will be better than 24*12*12
2)
Quote:
Old Volume= LWH Old Price= P -> Volume/Price=LWH/P
New Volume= LWH(1-50/100)= LWH/2 New Price=P/2 -> Volume Price=LWH/P

where you hav egone wrong is that we are doing 50% of EACH dimension and not the VOLUME..
New Volume= LWH(1-50/100)(1-50/100)(1-50/100)= LWH/8 New Price=P/2 -> Volume Price=(LWH/8)/(P/2)=2LWH/8P=lwh/4p
lwh/4p is 4 times of lwh/p so extra paid is 4-1 = 3 times and hence 300%..

Got it, thanks for the clarification chetan2u
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To save money, Arkadelphia Cream Cheese will reduce each dimension of  [#permalink]

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If the current volume is $$L * W * H$$,

then the new volume is

$$\frac{1}{2} (L) * \frac{1}{2} (W) * \frac{1}{2} (H), or \frac{1}{8} * LWH.$$

So the new portion is $$\frac{1}{8}$$ the size of the old portion. But the new cost is only $$\frac{1}{2}$$ the cost, meaning that if the old price-per-unit was 1:1, now it’s $$\frac{1}{2} : \frac{1}{8}$$ , or 4:1.

So the consumer is paying 400% of what it used to, or 300% more than it used to.

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Please award kudos, If this post helped you in someway.  To save money, Arkadelphia Cream Cheese will reduce each dimension of   [#permalink] 02 Oct 2018, 02:28
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