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Veritas PS Practice Q8

This topic has 4 expert replies and 0 member replies
rbakerv Newbie | Next Rank: 10 Posts Default Avatar
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Veritas PS Practice Q8

Post Tue Feb 24, 2015 2:56 pm
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%

Veritas Answer is: D

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sanju09 GMAT Instructor
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Post Wed Feb 25, 2015 11:13 pm
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?

No change
50%
100%
300%
400%

Veritas Answer is: D
Let’s deal with easy numbers only. Take each dimension of box as 10 inches, so that its volume is 1000 cubic inches, which costs a consumer 2000 cents (say), such that the original cost per cubic inch is 2 cents.

Next scene, each dimension of box is made 5 inches, so that its volume now is 125 cubic inches. Then reduce the price it charges its consumers to 1000 cents so that the cost per cubic inch now is 1000/125 = 8 cents per cubic inch.

Evidently, the percent increase in price-per-cubic-inch = [(8 - 2)/2] X 100% = 300%

(D) is right.

_________________
The mind is everything. What you think you become. –Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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Top Reply
Post Tue Feb 24, 2015 6:37 pm
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

_________________
Contact Rich at Rich.C@empowergmat.com

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GMAT/MBA Expert

sanju09 GMAT Instructor
Joined
21 Jan 2009
Posted:
3650 messages
Followed by:
81 members
Upvotes:
267
GMAT Score:
760
Post Wed Feb 25, 2015 11:13 pm
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?

No change
50%
100%
300%
400%

Veritas Answer is: D
Let’s deal with easy numbers only. Take each dimension of box as 10 inches, so that its volume is 1000 cubic inches, which costs a consumer 2000 cents (say), such that the original cost per cubic inch is 2 cents.

Next scene, each dimension of box is made 5 inches, so that its volume now is 125 cubic inches. Then reduce the price it charges its consumers to 1000 cents so that the cost per cubic inch now is 1000/125 = 8 cents per cubic inch.

Evidently, the percent increase in price-per-cubic-inch = [(8 - 2)/2] X 100% = 300%

(D) is right.

_________________
The mind is everything. What you think you become. –Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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Post Tue Feb 24, 2015 6:37 pm
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

_________________
Contact Rich at Rich.C@empowergmat.com

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