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Re: What is the ratio of a to b to c ? [#permalink]

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28 Apr 2013, 11:37

Zarrolou wrote:

What is the ratio of a to b to c ?

\(a/b/c=\frac{a}{bc}\)

I don't think that this is correct ?! all we know is the ratio of a to b is a/b .. that's why you must assign a new variable x and refer to it as smyarga did

It is the correct way to do this
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Re: What is the ratio of a to b to c ? [#permalink]

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28 Apr 2013, 11:48

Rock750 wrote:

I don't think that this is correct ?! all we know is the ratio of a to b is a/b .. that's why you must assign a new variable x and refer to it as smyarga did

It is the correct way to do this

My point is : the ratio a to b is a division a/b The ration a to b is 2 means a/b=2 the ration (a to b) to c is also a division (I don't see why it sould not be). That's why I do not agree, maybe I have to review ratios Look at the real numbers , all respect A. a=20 , b= 80 c=50 a:b:c=1/200 a=8 , b=32 c=20 a:b:c=1/80
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Re: What is the ratio of a to b to c ? [#permalink]

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28 Apr 2013, 11:54

Zarrolou wrote:

Rock750 wrote:

I don't think that this is correct ?! all we know is the ratio of a to b is a/b .. that's why you must assign a new variable x and refer to it as smyarga did

It is the correct way to do this

My point is : the ratio a to b is a division a/b The ration a to b is 2 means a/b=2 the ration (a to b) to c is also a division (I don't see why it sould not be). That's why I do not agree, maybe I have to review ratios Look at the real numbers , all respect A. a=20 , b= 80 c=50 a:b:c=1/200 a=8 , b=32 c=20 a:b:c=1/80

in your opinion, why should ratio of a to b to c equal to (a to b) to c and not equal to a to (b to c) ? we don't know if the operation "to" is transitive ..
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Last edited by Rock750 on 28 Apr 2013, 12:28, edited 1 time in total.

Re: What is the ratio of a to b to c ? [#permalink]

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28 Apr 2013, 11:59

Rock750 wrote:

in your opinion, why should ratio of a to b to c equal to (a to b) to c and not equal to a to (b to c) ? we don't know if the operation "to" is commutative ..

I think we are going nowhere here but in my opinion we should not forget the meaning of ratio: it's a division 5:5:5=0.2 is equal to (5:5):5=0,2 and not to 5:(5:5)=5
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Re: What is the ratio of a to b to c ? [#permalink]

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28 Apr 2013, 12:00

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Zarrolou, in your examples the ratio is the same. a=20 , b= 80 c=50 a:b:c=20:80:50=2:8:5 a=8 , b=32 c=20 a:b:c=8:32:20=2:8:5 You shouldn't mix them. Here is relative ratio of three numbers together. The ratio of three numbers a:b:c=n:m:k just means that there some integer x such that a=nx, b=mx, c=kx.
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Re: What is the ratio of a to b to c ? [#permalink]

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28 Apr 2013, 12:02

Zarrolou wrote:

Rock750 wrote:

in your opinion, why should ratio of a to b to c equal to (a to b) to c and not equal to a to (b to c) ? we don't know if the operation "to" is commutative ..

I think we are going nowhere here but in my opinion we should not forget the meaning of ratio: it's a division 5:5:5=0.2 is equal to (5:5):5=0,2 and not to 5:(5:5)=5

the ratio of 5:5:5 is equal to 1:1:1
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Re: What is the ratio of a to b to c ? [#permalink]

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28 Apr 2013, 12:04

For example, the ratio of the number of women to the number of men to the number of children is 1 to 2 to 3. Your ratio as 1 to 80 is meaningless, because you compare 3 objects and as result have comparison of two objects.
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Re: What is the ratio of a to b to c ? [#permalink]

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27 Jun 2013, 05:49

Rock750 wrote:

What is the ratio of a to b to c ?

(1) \(\frac{c}{a} =\frac{5}{2}\) and \(b=4a\)

(2) \(ac = 40\) and \(b=16\)

st.1

a/c = 2/5, a/b = 1/4. to put these 3 in ratio we've to equate the common thing i.e. a. it'll become a/c=2/5 and a/b=2/8. << I equated a in both the expression by multiplying and dividing 2 a:b:c=2:8:5. simple.

st.2

It will clearly wont give the desired rsult.
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(1) \(\frac{c}{a} =\frac{5}{2}\) and \(b=4a\). From \(b=4a\), we have the \(\frac{a}{b}=\frac{1}{4}=\frac{2}{8}\). So, we have that a:c=2:5 and a:b=2:8 --> a:b:c=2:8:5. Sufficient.

(2) \(ac = 40\) and \(b=16\). Not sufficient.

Answer: A.

As for your solution: the ratio is the same! You have a:b:c = a:4a:(2.5a) --> a reduces: a:b:c = 1:4:(2.5), which is the same ratio as a:b:c = 2:8:5 = 4:16:10 = 8:32:20 ...

Re: What is the ratio of a to b to c ? [#permalink]

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27 Jun 2013, 08:19

First of all thank you members, But little confusion still remains, as long as I see this sum in isolation everything is clear but when I try and relate this sum to this sum given below I get a bit confused.

\(so \, for \, Y=1 \to x:y:z =\frac {\frac{14}{1}}{21}\)

and \(for \, Y=7 \to x:y:z =\frac {\frac{2}{7}}{3}\)

now using the same logic as above where we said "a reduces" and said that the ratio remains the same, can't we say in this sum too that ( x:y:z ) "Y reduces" hence 1+2 is sufficient to answer the ratio of x:y:z ?

if in a:b:c sum we say " as a:b:c = 2:8:5 = 4:16:10 = 8:32:20 ... " meaning in all the cases ratio is same

why in x:y:z = 14:1:21 and x:y:z = 2:7:3 , we are taking ratio to be different? shouldn't the ratio be same whether x:y:z= 14:1:21 or x:y:z = 2:7:3

we can say Y can be reduced and that 14:1:21 is the same as 2:7:3 answer should be C in this x:y:z sum, still here the answer is E. ?? Am I messing up something? Thanks.

Edit: my bad didn't see that 14:1:21 cannot be reduced to 2:7:3 so of course the answer is E
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Last edited by stne on 02 Sep 2013, 23:03, edited 1 time in total.

Re: What is the ratio of a to b to c ? [#permalink]

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27 Jun 2013, 08:29

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stne wrote:

First of all thank you members, But little confusion still remains, as long as I see this sum in isolation everything is clear but when I try and relate this sum to this sum given below I get a bit confused.

\(so \, for \, Y=1 \to x:y:z =\frac {\frac{14}{1}}{21}\)

and \(for \, Y=7 \to x:y:z =\frac {\frac{2}{7}}{3}\)

now using the same logic as above where we said "a reduces" and said that the ratio remains the same, can't we say in this sum too that ( x:y:z ) "Y reduces" hence 1+2 is sufficient to answer the ratio of x:y:z ?

if in a:b:c sum we say " as a:b:c = 2:8:5 = 4:16:10 = 8:32:20 ... " meaning in all the cases ratio is same

why in x:y:z = 14:1:21 and x:y:z = 2:7:3 , we are taking ratio to be different? shouldn't the ratio be same whether x:y:z= 14:1:21 or x:y:z = 2:7:3

we say say Y can be reduced and that 14:1:21 is the same as 2:7:3 answer should be C in this x:y:z sum, still here the answer is E. ?? Am I messing up something? Thanks.

Re: What is the ratio of a to b to c ? [#permalink]

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27 Jun 2013, 08:51

@stunn3r

Thank you, equating the common variable seems to make sense , doing it my way where I was expressing everything in terms of a single variable , does not seem to work here. Thank you
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Re: What is the ratio of a to b to c ? [#permalink]

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01 Jul 2014, 00:53

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