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OG PS 11

This topic has 5 expert replies and 1 member reply
paml Junior | Next Rank: 30 Posts Default Avatar
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OG PS 11

Post Sat Feb 07, 2015 12:43 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    OG 13th ed/2015
    p. 153
    Problem Solving Practice Question #11.

    When Leo imported a certain item, he paid a 7% import tax on the portion of the total value of the item in excess of $1000. If the amount of the import tax that Leo paid was $87.50 what was the total value of the item?
    A $1600
    B $1850
    C $2250
    D $2400
    E $2750

    I don't quite understand this part of the question and how to set it up properly: "7% import tax on the portion of the total value of the item in excess of $1000". I'm not clear on what the italicized portion means.

    Is it saying he paid a 7% import tax on the $1000 portion of the item? The answer explanation sets it up as .07(t - 1000)

    The way I set it up was .07x = 87.5
    x=1250
    Then I just added 1000 and got the answer C: 2250
    Is this a wrong/bad way of setting it up?

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    Post Sat Feb 07, 2015 12:53 pm
    paml wrote:
    When Leo imported a certain item, he paid a 7% import tax on the portion of the total value of the item in excess of $1000. If the amount of the import tax that Leo paid was $87.50 what was the total value of the item?
    A $1600
    B $1850
    C $2250
    D $2400
    E $2750
    We can PLUG IN THE ANSWERS, which represent the total value of the item.
    When the correct answer choice is plugged in, the tax will be $87.50.

    Answer choice D: 2400
    Portion in excess of 1000 = 2400-1000 = 1400.
    7% tax on this portion = (7/100)(1400) = 98.
    Since the tax is too great, the correct answer choice must be smaller.
    Eliminate D and E.

    Answer choice B: 1850
    Portion in excess of 1000 = 1850-1000 = 850.
    7% tax on this portion = (7/100)(850) ≈ 60.
    Since the tax is too small, the correct answer choice must be greater.
    Eliminate A and B.

    The correct answer is C.

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    Post Sat Feb 07, 2015 12:59 pm
    paml wrote:
    I don't quite understand this part of the question and how to set it up properly: "7% import tax on the portion of the total value of the item in excess of $1000". I'm not clear on what the italicized portion means.
    In other words, the first $1000 is "free" (there's no tax).
    So, for example, if the TOTAL value is $800, then there's no tax charged.
    Likewise, if the TOTAL value is $1000, then there's no tax charged.

    However, if the TOTAL value were $1100, then Leo would pay 7% on $100 (since $1100 EXCEEDS $1000 by $100)
    If the TOTAL value were $1600, then Leo would pay 7% on $600 (since $1600 EXCEEDS $1000 by $600)

    Cheers,
    Brent

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    Post Sat Feb 07, 2015 1:02 pm
    paml wrote:
    When Leo imported a certain item, he paid a 7% import tax on the portion of the total value of the item in excess of $1000. If the amount of the import tax that Leo paid was $87.50 what was the total value of the item?
    A $1600
    B $1850
    C $2250
    D $2400
    E $2750

    I don't quite understand this part of the question and how to set it up properly: "7% import tax on the portion of the total value of the item in excess of $1000". I'm not clear on what the italicized portion means.

    Is it saying he paid a 7% import tax on the $1000 portion of the item? The answer explanation sets it up as .07(t - 1000)

    The way I set it up was .07x = 87.5
    x=1250
    Then I just added 1000 and got the answer C: 2250
    Is this a wrong/bad way of setting it up
    ?
    Your solution is fine. It's pretty much the same as the official solution, except you're not showing all of the steps (i.e., you're making a few moves in your head)

    Cheers,
    Brent

    _________________
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    Use our video course along with Beat The GMAT's free 60-Day Study Guide

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    Post Sat Feb 07, 2015 1:14 pm
    paml wrote:
    When Leo imported a certain item, he paid a 7% import tax on the portion of the total value of the item in excess of $1000. If the amount of the import tax that Leo paid was $87.50 what was the total value of the item?
    A $1600
    B $1850
    C $2250
    D $2400
    E $2750
    Here's a step-by-step algebraic solution.

    Let T = the TOTAL value of the item.

    Leo paid a 7% import tax on the portion of the total value of the item in EXCESS of $1000
    So, Leo pays tax on the amount that's GREATER then $1000
    So, Leo pays 7% tax on (T - 1000)
    We can write: import tax = 7% of (T - 1000)

    The amount of the import tax that Leo paid was $87.50
    So, we write: $87.50 = 7% of (T - 1000)
    Or: $87.50 = 0.07(T - 1000)
    Expand to get: 87.50 = 0.07T - 70
    Add 70 to both sides to get: 157.5 = 0.07T

    NOTE: At this point, you might just plug in the answer choices to see which one makes the above equation true.
    Or....
    Divide both sides by 0.07 to get: 157.5/0.07 = T
    Solve: 2250 = T

    Answer: C

    Cheers,
    Brent

    _________________
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    paml Junior | Next Rank: 30 Posts Default Avatar
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    Post Sat Feb 07, 2015 2:26 pm
    Thank you Brent & Mitch!

    GMAT/MBA Expert

    Post Sun Feb 08, 2015 10:18 pm
    Another approach here!

    Suppose the item cost Leo $x. We know that the first $1000 is tax free, so Leo only pays 7% tax on the rest of the price, or $(x - 1000). We know that tax amounted to $87.50, so we have

    87.50 = 7% of (x - 1000), or
    87.5 = .07(x - 1000), or
    87.5 = .07x - 70, or
    157.5 = .07x, or
    15750 = 7x, or
    2250 = x

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