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Need a quick explanation please.

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Source: — Data Sufficiency |
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by aim-wsc » 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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by gklick » 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.
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by gklick » 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)
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Componendo & Dividendo Principle

by Rishabh » 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
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by aim-wsc » 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 :x :evil: :cry:

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

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

btw, Principle of Alternendo - was there any ?
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by aim-wsc » Tue Aug 29, 2006 11:53 pm
lol

:lol:

if a/b= x/y

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

basic indeed.:shock:
got to refresh...
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