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Need a quick explanation please.

This topic has 7 member replies
gklick Newbie | Next Rank: 10 Posts Default Avatar
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Posted:
5 messages

Need a quick explanation please.

Post Sun Aug 27, 2006 3:15 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    See the attached file. The correct answer is B.
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    aim-wsc Legendary Member
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    Post Sun Aug 27, 2006 4:51 pm
    m/r & x/y are the ratios we are looking for.

    which may or may not be equal; depending on the condition

    condition A) m/r = x/r

    lets give these guys figures-value
    randomly so they follow condition A)

    m=20
    y=5
    note i hv taken m 4 times to y
    therefore x hs to be 4 times to r
    in order to satisfy the condition A.

    x=28
    r=7

    now check for
    ratios
    m/r=20/7
    & x/y=28/5

    you can see that desired ratios are not equal.
    OK that gives you the answer that condtion A helps you decide right? NO
    what if i take values like
    x=40 & r=10?
    then you see that ratios m/r & x/y are equal

    that means condition A alone isnt sufficient

    Sp. NOTE FOR DS items asking you yes or no answer:
    Is the ratio m to r equals to x to y?
    note that question starts with 'Is' & therefore for it accepts the answer in yes or no.
    hey hey Its not a human soul so he wont get disappointed if you answer him NO.
    in fact he would be satisfied that he got the answer anyway. be it yes or no.
    (this cocept is very tricky & mind you even most math rockers fall in this...they figure out whether conditions are enough or not but they fail to see that CAT asked them just to tell the answer. be it in positive or negative :condition satisfies & hence sufficient
    & undecisive then head for next condition: condition isnt sifficient.

    in this case: condition A is not sufficient.


    NOTE: FOR APPROACHING, THE WAY I HV CHECKED WITH CONDITION 'B'. I WANT YOU TO THINK ALONG. DONT JUST READ IT.
    ITS A PROCESS.


    Condition B
    (m+x)/(r+y)=x/y

    take
    x=12
    y =4
    (take any random number )

    therefore lets make (m+x) 3 times to the (r+y)
    while figuring out this you realise that you have to make 'm' 3 times to 'r' in any case to satisfy condition B

    i take m=9 & r=3
    so that m+x=21
    y+r=7

    you can check the desired ratios.
    m/r=9/3 & x/y=12/4

    satisfied. 8)

    [PS: my apologies for making my asnwer lengthy...you had asked for short one.]

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    gklick Newbie | Next Rank: 10 Posts Default Avatar
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    Post Sun Aug 27, 2006 5:08 pm
    Thanks, that does make sense. Any idea how to prove it mathematically w/o substitution? If no, that's okay, this explanation is better than no explanation.

    gklick Newbie | Next Rank: 10 Posts Default Avatar
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    Post Sun Aug 27, 2006 5:37 pm
    gklick wrote:
    Thanks, that does make sense. Any idea how to prove it mathematically w/o substitution? If no, that's okay, this explanation is better than no explanation.
    Actually, for some reason, I just got it. I have no idea why this was difficult initially.

    Given: (m + x) / (r + y) = x / y

    x (r + y) = y (m + x)
    xr + xy = my + xy
    xr = my
    (m/r) = (x/y)

    Rishabh Junior | Next Rank: 30 Posts Default Avatar
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    Post Tue Aug 29, 2006 4:10 am
    Hi,

    We have been given
    B) (m + x) / (r + y) = x / y
    and we have to check if m/r = x/y

    Soln: We can write
    m/r = x/y
    => m/x = r/y
    => m+x/x = r+y/y (Principle of componendo)
    => m+x/r+y = x/y - same as B

    Hence proced mathematically

    aim-wsc Legendary Member
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    Post Tue Aug 29, 2006 10:04 am
    thats right.

    & if you know that principle then you wouldnt hv asked the question in first place....


    but rishab, it s i think 8 grade high school math. isnt it?

    man !!!
    principles of Principle of componendo
    thats the term right>>?

    ok
    i m quite old now Mad Evil or Very Mad Crying or Very sad

    dont remember any highschool math.. Sad
    so i had to solve it emperically.

    bytheway....can you tell me Rishab,
    what theres some terms like alternando...dividendo.......sigh Exclamation
    i dont remember them now...they are all brothers right./?

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    Rishabh Junior | Next Rank: 30 Posts Default Avatar
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    Post Tue Aug 29, 2006 11:33 pm
    Hi,

    I remember only a few of them now...

    Principle of componendo:
    a/b = c/d
    => a+b/b = c+d/d

    Principle of dividendo:
    a/b = c/d
    => a-b/b = c-d/d

    and in ratios & proportions:
    a:b :: c:d
    product of means = product of extremes
    => a*d = b*c

    and GMAT tries to test on such things which actually are very basic..Sad

    btw, Principle of Alternendo - was there any ?

    aim-wsc Legendary Member
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    Post Tue Aug 29, 2006 11:53 pm
    lol

    Laughing

    if a/b= x/y

    a+b / a-b = x+y / x-y

    basic indeed.Shocked
    got to refresh...

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