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Math Help - GMAT Algebra Help

  1. #1
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    GMAT Algebra Help

    Here's a question on my GMAT study book that I really don't know how to figure out...

    Could someone show me HOW to work this out? And/Or the most effective way to figure it out?


    2 3
    if --- + --- = 4 and xy = 5, then 3x + 2y = ?
    x y

    crap, the formatting isn't there...

    try this
    if (2/x) + (3/y) = 4 and xy = 5, then 3x + 2y
    Last edited by matoau; April 3rd 2008 at 08:20 AM. Reason: edited to show formula, since forum reformats text
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  2. #2
    Oli
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    Multiply left handside of equation one by xy, RHS by 5. (since xy=5 we can do this and equality still holds).

    We get 2y +3x = 20
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  3. #3
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    Quote Originally Posted by matoau View Post
    Here's a question on my GMAT study book that I really don't know how to figure out...

    Could someone show me HOW to work this out? And/Or the most effective way to figure it out?


    2 3
    if --- + --- = 4 and xy = 5, then 3x + 2y = ?
    x y

    \frac{2}{x}+\frac{3}{y}=4

    if multiply by lcd xy we get

    (xy)\left( \frac{2}{x}+\frac{3}{y} \right)=4(xy) \iff 2y+3x=4 \cdot \underbrace{xy}_{equals 5}

    so 2y+3x=20
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  4. #4
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    Quote Originally Posted by Oli View Post
    Multiply left handside of equation one by xy, RHS by 5. (since xy=5 we can do this and equality still holds).

    We get 2y +3x = 20
    So:

    2 * 5 = 10
    3 * 5 = 15
    ------------
    25

    ?? Not following.
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  5. #5
    Oli
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    2/x +3/y = 4
    xy=5

    Multiply both sides by xy:
    (xy)*(2/x + 3/y) = 4xy
    Which implies:
    2y + 3x = 4xy
    But xy = 5 so:
    2y + 3x = 4*5 = 20
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  6. #6
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    Quote Originally Posted by TheEmptySet View Post
    \frac{2}{x}+\frac{3}{y}=4

    if multiply by lcd xy we get

    (xy)\left( \frac{2}{x}+\frac{3}{y} \right)=4(xy) \iff 2y+3x=4 \cdot \underbrace{xy}_{equals 5}

    so 2y+3x=20
    Oh, ok...

    So to clarify...

    2y + 3x = 4 (here we basically took the denominator of the others fraction)

    we already know xy = 5

    so we simply multiply 4 * 5 and get 20?
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  7. #7
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    Is it this simple?

    if 2/x + 3y = 4 and xy = 5, then 3x + 2y = ??


    2x + 3y = 4(xy)


    2y + 3x = 4(5)


    2y + 3x = 20


    also:
    how are you making these nice equations all nice and formatted?
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  8. #8
    Oli
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    Your second line isn't true.

    You have to multiply both sides of the equation by xy.

    b=c

    =>

    ab=ac
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  9. #9
    Oli
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    That is an absolute crippler, if you don't know that you will die at a young age.
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  10. #10
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    is there somewhere I can plug this into to see the entire problem worked out? that's the only way i'm going to be able to figure this out without a math wiz sitting right next to me.

    a? b? c?

    we're dealing with x & y here...

    b=c

    =>

    ab=ac
    what's this mean:
    "That is an absolute crippler, if you don't know that you will die at a young age."
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  11. #11
    Oli
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    The a,b,c stuff was just showing how you manipulate equations.

    You have to do the same thing to both sides, otherwise the equality doesn't hold.
    Examples:
    x=y implies x+5=y+5
    x=y implies 3x=3y
    x + y = 6 implies 6(x+y)=6*6 implies 6x + 6y = 36
    Absolutely crucial you understand the above or you will never ever be able to solve any maths problems.

    In your second line you wrote:
    2/x + 3/y = 4 implies 3/x + 3/y = 4xy
    This is not true.


    You should have written:
    2/x + 3/y = 4 implies (2/x + 3/y)xy = 4xy
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  12. #12
    Behold, the power of SARDINES!
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    Quote Originally Posted by matoau View Post
    Is it this simple?

    if 2/x + 3y = 4 and xy = 5, then 3x + 2y = ??


    2x + 3y = 4(xy)


    2y + 3x = 4(5)


    2y + 3x = 20


    also:
    how are you making these nice equations all nice and formatted?

    It is called La Tex and here is a link on how to use it.

    http://en.wikipedia.org/wiki/Help Formula

    Also if you hover you mouse over someone elses code it will show up, or you can double click on it.
    Good luck.
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  13. #13
    Oli
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    The whole problem, with the logic written between lines:
    We know
    1. 2/x + 3/y = 4
    2. xy = 5

    2/x + 3/y = 4
    (since a=b implies ac = bc)
    =>(2/x + 3/y)xy = 4xy
    (since a(b+c) = ab +ac)
    => 2xy/x + 3xy/y = 4xy
    (since a/a = 1)
    => 2y + 3x = 4xy
    (since xy = 5 from equation 2)
    => 2y + 3x = 4*5
    (since 4*5=20)
    => 2y + 3x = 20
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  14. #14
    Oli
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    Did you edit that post that started "is it this simple..."?

    I think I am going crazy, whatever. That post is absolutely correct, it is that simple. Thought you wrote something different...
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  15. #15
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    Quote Originally Posted by Oli View Post
    Did you edit that post that started "is it this simple..."?

    I think I am going crazy, whatever. That post is absolutely correct, it is that simple. Thought you wrote something different...
    i didn't edit it... so it is that simple? I edited the text directly below... 2/x + 3/x

    Is it this simple?

    if 2/x + 3/y = 4 and xy = 5, then 3x + 2y = ??


    2x + 3y = 4(xy)


    2y + 3x = 4(5)


    2y + 3x = 20
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