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sukh Rising GMAT Star
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difficult questions Post Sat Sep 03, 2011 7:54 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    MaryÂ's annual income is $15,000 and JohnÂ's annual income is
    $18,000. By how much must MaryÂ's annual income increase
    so that it constitutes 55% of Mary and JohnÂ's combined
    income?
    (A) $3,000
    (B) $4,000
    (C) $7,000
    (D) $11,000
    (E) $25,000
    Answer C
    Decreasing the original price of an item by 25% and then
    decreasing the new price by z% is equivalent to decreasing
    the original price by

    (A) 0.25(1 + 3z/100 )

    (B) 0.25(1 + z/100 )

    (C) 0.25(1 - 3z /100 )

    (D) 0.75(1 - z/100 )

    (E) 0.75(1 + 3z/100 )

    Answer A

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    n@resh Rising GMAT Star Default Avatar
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    Post Sat Sep 03, 2011 12:23 pm
    sukh wrote:
    MaryÂ's annual income is $15,000 and JohnÂ's annual income is
    $18,000. By how much must MaryÂ's annual income increase
    so that it constitutes 55% of Mary and JohnÂ's combined
    income?
    (A) $3,000
    (B) $4,000
    (C) $7,000
    (D) $11,000
    (E) $25,000
    Answer C
    Decreasing the original price of an item by 25% and then
    decreasing the new price by z% is equivalent to decreasing
    the original price by

    (A) 0.25(1 + 3z/100 )

    (B) 0.25(1 + z/100 )

    (C) 0.25(1 - 3z /100 )

    (D) 0.75(1 - z/100 )

    (E) 0.75(1 + 3z/100 )

    Answer A
    We don't have any answer for 1st Question. Ans is 3150 as 55%*33000 leads to 18150!

    for 2nd: Option A is the right Ans.

    As we know 0.75 - 0.75*Z/100 => 1 - ( 0.25 + 0.75*z/100 )

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    Post Wed Sep 07, 2011 1:08 pm
    sukh wrote:
    MaryÂ's annual income is $15,000 and JohnÂ's annual income is
    $18,000. By how much must MaryÂ's annual income increase
    so that it constitutes 55% of Mary and JohnÂ's combined
    income?
    (A) $3,000
    (B) $4,000
    (C) $7,000
    (D) $11,000
    (E) $25,000
    We can plug in the answers, which represent the needed increase in Mary's income.

    Answer choice C: 7,000.
    Increased income for Mary = 7000+15,000 = 22,000.
    New total income for Mary and John = 22,000+18,000 = 40,000.
    Mary/Total = 22,000/40,000 = 11/20 = 55%.
    Success!

    The correct answer is C.

    Quote:
    Decreasing the original price of an item by 25% and then
    decreasing the new price by z% is equivalent to decreasing
    the original price by

    (A) 0.25(1 + 3z/100 )

    (B) 0.25(1 + z/100 )

    (C) 0.25(1 - 3z /100 )

    (D) 0.75(1 - z/100 )

    (E) 0.75(1 + 3z/100 )
    Let original price = 100.
    Price decreased by 25% = 100-25 = 75.
    Let z=20.
    Price further decreased by 20% = 75 - .2(75) = 60.
    Total decrease = 100-60 = 40.
    Decrease/Original = 40/100.

    Now we plug z=20 into the answers to see which yields our target of 40/100.

    Only answer choice A works:
    0.25(1 + 3z/100)
    = (1/4)(1 + (3*20)/100)
    = (1/4)(160/100)
    = 40/100.

    The correct answer is A.

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