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Percentage of income

This topic has 5 expert replies and 1 member reply
GmatGreen Senior | Next Rank: 100 Posts Default Avatar
Joined
31 Mar 2009
Posted:
85 messages

Percentage of income

Post Thu Feb 13, 2014 10:46 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Mary's income is 60 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. what percent of Juan's income is Mary's income?

    A) 124%

    B) 120%

    C) 96%

    D) 80%

    E) 64%

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    GMAT/MBA Expert

    Post Thu Feb 13, 2014 10:57 am
    One approach is to plug-in values. Since the Q asks for Mary's as a % of Juan's income, it would be easiest to make J=100 and go from there. Tim's is 40% less than Juan, so T=60. Mary's is 60% more than Tim so M=60+36=96. M=96 and J=100, so Mary's is 96% of Tim's

    Another approach is algebraic. The full solution below is taken from the GMATFix App.



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    Post Thu Feb 13, 2014 10:59 am
    GmatGreen wrote:
    Mary's income is 60 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. what percent of Juan's income is Mary's income?

    A) 124%
    B) 120%
    C) 96%
    D) 80%
    E) 64%
    I suggest that we choose some nice values that meet the given conditions.

    Tim's income is 40 percent less than Juan's income.
    Let Juan's income = $100
    40% of $100 = $40
    This means Tim's income = $100 - $40 = $60

    Mary's income is 60 percent more than Tim's income
    60% of $60 = $36
    So Mary's income = $60+ $36 = $96

    What percent of Juan's income is Mary's income?
    Juan's income = $100
    Mary's income = $96

    So, Mary's income is 96% of Juan's income
    Answer: C

    Cheers,
    Brent

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    Post Thu Feb 13, 2014 11:52 am
    Hi GmatGreen,

    Both Brent and Patrick have provided an explanation that focuses on TESTing Values; I'm a big fan of this approach and I highly recommend it. As an alternative, here's the algebra approach:

    We'll need to translate the "math phrases" into actual equations.

    "Mary's income is 60% more than Tim's income"

    M = 1.6T

    "Tim's income is 40% less than Juan's income"

    T = .6J

    "What percent of Juan's income is Mary's income?"

    We already have a value for M (above); now we need to take the second equation and solve for J…

    T = .6J
    T = 3J/5
    5T/3 = J

    We're asked for the value of M/J….

    M = 1.6T
    J = 1.666T

    1.6T/1.666T = 1.6/1.666 = a little less than 1

    The only answer that's close is answer C

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    Post Mon Jun 29, 2015 7:06 am
    GmatGreen wrote:
    Mary's income is 60 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. what percent of Juan's income is Mary's income?

    A) 124%

    B) 120%

    C) 96%

    D) 80%

    E) 64%
    Solution:

    To solve this problem we define variables for the incomes of Mary, Tim, and Juan, and then set up some equations.

    T = Tim’s income

    M = Mary’s income

    J = Juan’s income

    We are given that Mary’s income is 60% more than Tim’s. Thus, we can say:

    M = 1.6T

    We are also given that Tim’s income is 40% less than Juan’s income. So we can say:

    T = 0.6J

    We are asked to determine the percent of Juan’s income that Mary’s income is. For this we can set up the expression:

    M/J x 100%

    To complete this problem we must express Juan’s income and Mary’s income in terms of a common variable. That common variable is T. Thus, we have:

    M = 1.6T

    J = T/0.6

    So finally we can substitute T/0.6 for J and 1.6T for M

    M/J x 100%

    (1.6T)/(T/0.6) x 100%

    (1.6T) x (0.6/T) x 100%

    The T’s cancel and we have:

    1.6 x 0.6 x 100%

    0.96 x 100% = 96%

    Answer:C

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    Post Mon Jun 29, 2015 7:19 am
    GmatGreen wrote:
    Mary's income is 60 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. what percent of Juan's income is Mary's income?

    A) 124%

    B) 120%

    C) 96%

    D) 80%

    E) 64%
    Alternate approach:

    Ratios can be MULTIPLIED TOGETHER:
    M/J = M/T * T/J.
    In the equation above, the values in red CANCEL OUT.

    Mary's income is 60 percent more than Tim's income.
    Thus:
    M/T = 160/100 = 8/5.

    Tim's income is 40 percent less than Juan's income.
    Thus:
    T/J = 60/100.

    Since M/J = M/T * T/J, we get:
    M/J = 8/5 * 60/100 = 8/1 * 12/100 = 96/100 = 96%.

    The correct answer is C.

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    GMAT/MBA Expert

    Post Mon Jun 29, 2015 3:28 pm
    Algebra works too:

    M = T + .6T = 1.6T
    T = J - .4J = .6J

    So M = 1.6T = 1.6(*6J) = .96J

    and we're done!

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