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If x and y are positive integers and 1 + x + y + xy = 15 ...

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mitzwillrockgmat Really wants to Beat The GMAT! Default Avatar
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If x and y are positive integers and 1 + x + y + xy = 15 ... Post Thu May 20, 2010 2:24 am
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  • Lap #[LAPCOUNT] ([LAPTIME])
    If x and y are positive integers and 1 + x + y + xy = 15, what is the value of x + y?

    A. 3
    B. 5
    C. 6
    D. 8
    E. 9

    Please help explain this futher! I get to this point: (1 + x) (1 + y) =15 but what do i do further to get the answer 6?

    1 + x + y + xy = 15
    1 + x + y(1 + x) =15
    (1+x)(1+ y)=15

    now what?? thank you! Smile

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    liferocks GMAT Destroyer! Default Avatar
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    Post Thu May 20, 2010 2:32 am
    1 + x + y + xy = 15
    or (1+x)(1+y)=15
    15 can be expressed as multiple of two integers as (1,15)and (3,5)

    if (1+x)(1+y)=1*15..1+x=1 or x=0 and y=14..so x+y=14
    if (1+x)(1+y)=3*5..1+x=3 or x=2 and y=4..so x+y=6

    only C is in ans choice
    ans option C

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    Last edited by liferocks on Thu May 20, 2010 2:42 am; edited 1 time in total

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    sanju09 GMAT Instructor
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    Post Thu May 20, 2010 2:37 am
    liferocks wrote:
    1 + x + y + xy = 15
    or (1+x)(1+y)=15
    15 can be expressed as multiple (or the product?) of two integers as (1,15)and (3,5)

    if (1+x)(1+y)=1*15..1+x=1 or x=0 and y=14..so x+y=14.............not applicable
    if (1+x)(1+y)=3*5..1+x=3 or x=2 and y=4..so x+y=6....now edited

    only C is in ans choice
    ans option C
    You need to get rid of this...good to see that you have edited while I was quoting your work, and why did you use the spoiler function above?

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    liferocks GMAT Destroyer! Default Avatar
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    Post Thu May 20, 2010 2:42 am
    sanju09 wrote:
    liferocks wrote:
    1 + x + y + xy = 15
    or (1+x)(1+y)=15
    15 can be expressed as multiple (or the product?) of two integers as (1,15)and (3,5)

    if (1+x)(1+y)=1*15..1+x=1 or x=0 and y=14..so x+y=14.............not applicable
    if (1+x)(1+y)=3*5..1+x=3 or x=2 and y=4..so x+y=6....now edited

    only C is in ans choice
    ans option C
    You need to get rid of this...good to see that you have edited while I was quoting your work, and why did you use the spoiler function above?
    Now used the spoiler in both places

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    sanju09 GMAT Instructor
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    Post Thu May 20, 2010 2:48 am
    ...and what should be the correct wordings in this case?

    this: 15 can be expressed as multiple of two integers

    or that: 15 can be expressed as the product of two integers

    multiple and the product are two different words with different meanings in mathematics

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    liferocks GMAT Destroyer! Default Avatar
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    Post Thu May 20, 2010 2:51 am
    sanju09 wrote:
    ...and what should be the correct wordings in this case?

    this: 15 can be expressed as multiple of two integers

    or that: 15 can be expressed as the product of two integers
    Hmm..second one is definitely right and conveys the meaning correctly..but technically first one is also correct if we take a multiplicity factor as 1 Very Happy

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    Post Thu May 20, 2010 2:54 am
    liferocks wrote:
    sanju09 wrote:
    ...and what should be the correct wordings in this case?

    this: 15 can be expressed as multiple of two integers

    or that: 15 can be expressed as the product of two integers
    Hmm..second one is definitely right and conveys the meaning correctly..but technically first one is also correct if we take a multiplicity factor as 1 Very Happy
    postmortem is not carried out on living beings

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    kstv GMAT Destroyer! Default Avatar
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    Post Thu May 20, 2010 3:04 am
    if (1+x)(1+y) = 15
    and x any y are +ve integers
    then (1+x) (1+y) = 5*3 and not 15*1
    cos 1+x or 1+y = 1 implies x or y = 0
    if 1+x = 5
    1+y = 3
    it is not necessary to find the values of x and y seperately
    adding the two (1+x)+(1+y) = 8
    x+y = 6

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    sanju09 GMAT Instructor
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    Post Thu May 20, 2010 3:10 am
    kstv wrote:
    if (1+x)(1+y) = 15
    and x any y are +ve integers
    then (1+x) (1+y) = 5*3 and not 15*1
    cos 1+x or 1+y = 1 implies x or y = 0
    if 1+x = 5
    1+y = 3
    it is not necessary to find the values of x and y seperately
    adding the two (1+x)+(1+y) = 8
    x+y = 6
    your name was missing in the hit list of my Quant Commandos

    _________________
    “The most important thing in business is honesty, integrity, hard work… family… never forgetting where we came from.”

    “The loudest one in the room is the weakest one in the room.”

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    Tel: +91-522- 6002178
    Cell:+91-9670999928
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