Home Forums MBA GMAT two math problems

This topic contains 8 replies, has 6 voices, and was last updated by  auburn88 7 years, 10 months ago.

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  • #21988

    cavanbas
    Participant

    1. Given that 3-x1/2=(2x-7)1/2, what is x?
    (i.e., “1/2” means square root.)

    2. Given that x+y=11 and x1/2=y-5, solve for x and y.

    1. Ans. x=4 or 64.
    2. Ans. x=4, y=7; x=9, y=2.

    #27652

    y82benji
    Participant

    3 – sqrt[x] = sqrt[2x-7]
    square both sides
    (3-sqrt[x])(3-sqrt[x]) = ([2x-7]^0.5)^2
    multiply out on left, mulitply exponents on the right
    3*3 – 3*sqrt[x] – 3*sqrt[x] + sqrt[x]*sqrt[x] = [2x-7]^1
    simplify
    9 – 6*sqrt[x] + x = 2x – 7
    subtract 9 and x from both sides
    -6*sqrt[x] = x – 16
    square both sides
    36x = x^2 – 32x + 256
    subtract 36x from both sides
    x^2 – 68x + 256
    use quadratic
    get x = 4 or 64

    #27653

    y82benji
    Participant

    sqrt[x] = y – 5
    square both sides
    x = y^2 – 10y + 25
    then
    x + y = 11
    subtract y from both sides
    x = 11 – y
    substitute “x = 11 – y” in x = y^2 – 10y + 25
    11 – y = y^2 – 10y + 25
    subtract 11 and add y to both sides
    0 = y^2 – 9y + 14
    use quadratic to solve and get
    y = 2 or 7
    go back to “x + y = 11”
    x = 9 or 4

    #28130

    jello
    Participant

    For the 1st question, the answer should be ONLY 4, not 64.
    3-sqrt(64)=sqrt(2*64-7)
    3-8=sqrt(121)
    -5=11 which is incorrect.

    Hence, the answer is only 4

    #28132

    y82benji
    Participant

    No, 64 is still correct because the square root of 64 can be -8 or +8. If you take the square root of 64 to be -8 then you have 3 – -8 = 11 = sqrt(121)

    #28197

    liebenator
    Participant

    I should not have read this thread. Now I have a headache.[:(]

    #28200

    y82benji
    Participant

    Gotta love math. It’s just a language with more grammar than vocabulary!

    #36765

    kaushalasp
    Participant

    rightly said…all the best…

    #36928

    auburn88
    Participant

    I have a headache too Liebenator. That makes the case for starting at the end of a thread and reading up.

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