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Veritas PS Practice Q8

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rbakerv Just gettin' started! Default Avatar
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Veritas PS Practice Q8 Post Tue Feb 24, 2015 2:56 pm
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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?

    No change
    50%
    100%
    300%
    400%

    Veritas Answer is: D

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    Post Tue Feb 24, 2015 3:02 pm
    Quote:
    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 = e³ = 2³ = 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 = 1³ = 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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    Post Tue Feb 24, 2015 3:07 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?

    A) No change
    B) 50%
    C) 100%
    D) 300%
    E) 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: D

    Cheers,
    Brent

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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

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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.

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