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Last year the price per share of Stock X increased

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rsarashi Master | Next Rank: 500 Posts Default Avatar
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Last year the price per share of Stock X increased

Post Wed Apr 19, 2017 9:16 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Last year the price per share of Stock X increased by k percent and the earnings per share of Stock X increased by m percent, where k is greater than m. By what percent did the ratio of price per share to earnings per share increase, in terms of k and m?

    A. k/m %
    B. (k - m) %
    C. [100(k - m)] / (100 + k) %
    D. [100(k - m)] / (100 + m) %
    E. [100(k - m)] / (100 + k + m) %

    OAD

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    Post Wed Apr 19, 2017 9:21 am
    Quote:
    Last year the price per share of Stock X increased by k percent and the earnings per share of Stock X increased by m percent, where k is greater than m. By what percent did the ratio of price per share to earnings per share increase, in terms of k and m?

    A) k/m%
    B) (k-m)%
    C) 100(k-m)/100+k %
    D) 100(k-m)/100+m %
    E) 100(k-m)/100+k+m %
    One approach is to plug in values.

    Let $100 be the original price per share of Stock X
    Choose a "nice" value for k. How about k = 200
    So, after a 200% increase, the new price per share = $300

    Let $100 be the original earnings per share of Stock X
    Choose a "nice" value for m. How about m = 100
    So, after a 100% increase, the new earnings per share = $200

    Original ratio of price/earnings = $100/$100 = 1
    New ratio of price/earnings = $300/$200 = 1.5

    By what percent did the ratio of price per share to earnings per share increase?
    So, the percent increase (from 1 to 1.5) is 50%.
    In other words, when k = 200 and m = 100, the ratio increases 50%

    Now, plug in 200 for k, and 100 for m, and look for the answer choice that also yields 50%.

    A. k/m = 200/100 = 2 (nope)

    B. (k - m) = 200 - 100 = 100 (nope)

    C. [100(k - m)] / (100 + k) = 10,000/300 = 33.333 (nope)

    D. [100(k - m)] / (100 + m) = 10,000/200 = 50 GREAT!

    E. [100(k - m)] / (100 + k + m) = 10,000/400 = 25 (nope)

    Answer: D

    Cheers,
    Brent

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    Post Wed Apr 19, 2017 10:31 am
    It's worth noting that on these types of questions, the correct answers seem to be disproportionately weighted towards D and E. (At least they are in the Official Guide - most test-takers will start with A and work their way down, so if the correct answer is D or E, the problem is more time consuming.) When I'm picking numbers, I like to start with E and work my way up.

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    Post Wed Apr 19, 2017 11:31 am
    rsarashi wrote:
    Last year the price per share of Stock X increased by k percent and the earnings per share of Stock X increased by m percent, where k is greater than m. By what percent did the ratio of price per share to earnings per share increase, in terms of k and m?

    A. k/m %
    B. (k - m) %
    C. [100(k - m)] / (100 + k) %
    D. [100(k - m)] / (100 + m) %
    E. [100(k - m)] / (100 + k + m) %

    OAD
    An alternate approach is to combine plugging in values with a bit of algebra.

    Old ratio:
    Let the original price = 100 and the original earnings = 100.
    Original ratio of price to earnings = 100/100 = 1.

    New ratio:
    Price increased by k% = 100 + (k/100)(100) = 100 + k.
    Earnings increased by m% = 100 + (m/100)(100) = 100 + m.
    New ratio = (100+k)/(100+m).

    Difference between the ratios:
    (100+k)/(100+m) - 1 = [(100+k) - (100+m)] / (100+m) = (k-m)/(100+m).

    Percent change in the ratios = (difference between the ratios)/(original ratio) * 100:
    [(k-m)/(100+m)] / 1 * 100 = [100(k-m)] / (100+m).

    The correct answer is D.

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