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

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mitzwillrockgmat Master | Next Rank: 500 Posts 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
Elapsed Time: 00:00
  • 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 Legendary Member 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

    Thanked by: mitzwillrockgmat

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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 Legendary Member 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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    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 Legendary Member 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 Legendary Member 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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    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

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