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a, b, c and N are four real numbers: a/(b+c) = b/(c+a) = c/(a+b) = N

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a, b, c and N are four real numbers: a/(b+c) = b/(c+a) = c/(a+b) = N  [#permalink]

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New post 08 Jan 2019, 21:32
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a, b, c and N are four real numbers such that:
a/(b+c) = b/(c+a) = c/(a+b) = N, such that (a+b+c) is not equal to 0.
Also M is a positive number. Is (M+N)/2 an odd integer?

(1) M = 3/2

(2) M = K/2, where K is an odd integer.
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Re: a, b, c and N are four real numbers: a/(b+c) = b/(c+a) = c/(a+b) = N  [#permalink]

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New post 09 Jan 2019, 05:19
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amanvermagmat wrote:
a, b, c and N are four real numbers such that:
a/(b+c) = b/(c+a) = c/(a+b) = N. Also M is a positive integer.
Is (M+N)/2 an odd integer?

(1) M = 3/2

(2) M = K/2, where K is an odd integer.



amanvermagmat

is the question posted correct?
in the question stem it says M is a +ve integer , but in #1 M is given as a fraction..
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Re: a, b, c and N are four real numbers: a/(b+c) = b/(c+a) = c/(a+b) = N  [#permalink]

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New post 09 Jan 2019, 21:53
Archit3110 wrote:
amanvermagmat wrote:
a, b, c and N are four real numbers such that:
a/(b+c) = b/(c+a) = c/(a+b) = N. Also M is a positive integer.
Is (M+N)/2 an odd integer?

(1) M = 3/2

(2) M = K/2, where K is an odd integer.



amanvermagmat

is the question posted correct?
in the question stem it says M is a +ve integer , but in #1 M is given as a fraction..


Thanks for pointing that out. Editing the question right now.
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Re: a, b, c and N are four real numbers: a/(b+c) = b/(c+a) = c/(a+b) = N  [#permalink]

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New post 09 Jan 2019, 23:42
amanvermagmat I still don't understand how statement 2 is not sufficient. M is definitely a positive non integer, since k is an odd integer and N = -1.

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Re: a, b, c and N are four real numbers: a/(b+c) = b/(c+a) = c/(a+b) = N  [#permalink]

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New post 10 Jan 2019, 00:14
1
amanvermagmat wrote:
a, b, c and N are four real numbers such that:
a/(b+c) = b/(c+a) = c/(a+b) = N. Also M is a positive number.
Is (M+N)/2 an odd integer?

(1) M = 3/2

(2) M = K/2, where K is an odd integer.


Hi amanvermagmat

Are you sure from the OA.

(1) M = 3/2

Let a=b=c=1...N= 1/2

M+N = 1/2 + 3/2= 4/2 = 2.........(M+N)/2 = 1..........Answer is Yes

Let a=1 b= 2 c=-3...N= -1

M+N = -1+ 3/2 = 1/2.........(M+N)/2 = 1/4................Answer is No

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Re: a, b, c and N are four real numbers: a/(b+c) = b/(c+a) = c/(a+b) = N  [#permalink]

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New post 10 Jan 2019, 02:09
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Mo2men wrote:
amanvermagmat wrote:
a, b, c and N are four real numbers such that:
a/(b+c) = b/(c+a) = c/(a+b) = N. Also M is a positive number.
Is (M+N)/2 an odd integer?

(1) M = 3/2

(2) M = K/2, where K is an odd integer.


Hi amanvermagmat

Are you sure from the OA.

(1) M = 3/2

Let a=b=c=1...N= 1/2

M+N = 1/2 + 3/2= 4/2 = 2.........(M+N)/2 = 1..........Answer is Yes

Let a=1 b= 2 c=-3...N= -1

M+N = -1+ 3/2 = 1/2.........(M+N)/2 = 1/4................Answer is No

Insufficient



Hello

Thanks for your query. I have again edited the question in light of this new information.

Well -if three or more ratios are equal, say p/q = r/s = t/u = .... (and so on)
then each of these ratios is also equal to = (p+r+t+...)/(q+s+u+...) , i.e., each of these ratios is equal to the ratio of sum of numerators and the sum of denominators.

So in my question: a/(b+c) = b/(c+a) = c/(a+b) = N.. Here N is also = (a+b+c)/(b+c+c+a+a+b) = (a+b+c)/2(a+b+c) .
Since a+b+c is coming in denominator, we CANNOT take those values where a+b+c = 0.
In your second example: a=1 b= 2 c=-3... a+b+c = 0 which is not allowed.

This should have been mentioned in the question, so I am editing now. Thanks for this query.
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Re: a, b, c and N are four real numbers: a/(b+c) = b/(c+a) = c/(a+b) = N  [#permalink]

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New post 10 Jan 2019, 02:22
amanvermagmat wrote:
Hello

Thanks for your query. I have again edited the question in light of this new information.

Well -if three or more ratios are equal, say p/q = r/s = t/u = .... (and so on)
then each of these ratios is also equal to = (p+r+t+...)/(q+s+u+...) , i.e., each of these ratios is equal to the ratio of sum of numerators and the sum of denominators.

So in my question: a/(b+c) = b/(c+a) = c/(a+b) = N.. Here N is also = (a+b+c)/(b+c+c+a+a+b) = (a+b+c)/2(a+b+c) .
Since a+b+c is coming in denominator, we CANNOT take those values where a+b+c = 0.
In your second example: a=1 b= 2 c=-3... a+b+c = 0 which is not allowed.

This should have been mentioned in the question, so I am editing now. Thanks for this query.


Hi amanvermagmat

Thanks for your reply and the nice rule that I learnt from you today.
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Re: a, b, c and N are four real numbers: a/(b+c) = b/(c+a) = c/(a+b) = N &nbs [#permalink] 10 Jan 2019, 02:22
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a, b, c and N are four real numbers: a/(b+c) = b/(c+a) = c/(a+b) = N

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