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Re: Ratio DS Question [#permalink]
25 Jun 2013, 13:39

On the Total GMAT book Sackmann explains that to find the values of x,y, and z we would need THREE equations and that to find the three part ratio x:y:z we would need TWO ratios. Can someone please elaborate on what exactly that means?

GK_Gmat wrote:

lumone wrote:

What is the ratio of x:y:z?

(1) xy=14 (2) yz=21

E.

Clear that 1 and 2 are insuff by themselves.

Together: x = 2, y = 7, z = 3 or x = 1, y = 14, z =21/14 insuff.

Re: What is the ratio of x:y:z? [#permalink]
25 Jun 2013, 21:33

2

This post received KUDOS

Expert's post

josemnz83 wrote:

I'm not quite sure. Perhaps someone can explain it to us. I also rewrote both proportions in terms of y.

dave785 wrote:

umm... I got C.

if x*y = 14, then x = 14 / y

if y*z = 21, then z = 21 / y

therefore, we can put the whole ratio in terms of y:

14/y : y : 21/y

why does this not work?

It doesn't work for the reason that there is a variable in the final expression. When the question is asking for the value of the ratio x:y:z, it means that we should get a unique numerical value with the given fact statement(s). One could plug in y = 1 and get the ratio as 14:1:21. Yet again, someone else might plugin y = 7 and get the ratio as 2:7:3. Thus the scope of getting two different numeric values makes it insufficient.

Re: What is the ratio of x:y:z? [#permalink]
26 Jun 2013, 12:08

How is this question different from a question that asks for the value of p if p=r/3q and then tells you that the value of r=2q? Is it because we can come up with an exact value for the equation?

I was under the impression that one needs to have three equations when dealing with three variables. Here we only have 2 equations (the original statement and r=2q?

mau5 wrote:

josemnz83 wrote:

I'm not quite sure. Perhaps someone can explain it to us. I also rewrote both proportions in terms of y.

dave785 wrote:

umm... I got C.

if x*y = 14, then x = 14 / y

if y*z = 21, then z = 21 / y

therefore, we can put the whole ratio in terms of y:

14/y : y : 21/y

why does this not work?

It doesn't work for the reason that there is a variable in the final expression. When the question is asking for the value of the ratio x:y:z, it means that we should get a unique numerical value with the given fact statement(s). One could plug in y = 1 and get the ratio as 14:1:21. Yet again, someone else might plugin y = 7 and get the ratio as 2:7:3. Thus the scope of getting two different numeric values makes it insufficient.

Re: What is the ratio of x:y:z? [#permalink]
26 Jun 2013, 22:29

1

This post received KUDOS

Expert's post

josemnz83 wrote:

How is this question different from a question that asks for the value of p if p=r/3q and then tells you that the value of r=2q? Is it because we can come up with an exact value for the equation?

Exactly. It is because you can get a unique numeric value for p. Also, with the help of these two equations, we can only solve for the value of only one variable, i.e. p, and nothing else.

Quote:

I was under the impression that one needs to have three equations when dealing with three variables. Here we only have 2 equations (the original statement and r=2q?

What you are saying is true, most of the times. However, there are times, when you have 3 equations and 3 variables and still get no unique solution, or get infinitely many solutions. Also, there are times when a single equation with 2 variables might give the value of both the variables under special conditions.[For example, when the variables can only assume integral values].

For example, 2x+3y=5, you can arrive at many integral solutions for (x,y) for example (1,1),(-2,3) etc. For the given context, there might be an additional restriction;like the value of both the variables should be positive,etc in the problem, which would then help you to zero-in on a unique solution. Ergo, it will be a good idea to keep in mind that apart from the general rule of N equations and N variables, there are many variants possible, depending on the context of the given problem.

Re: What is the ratio of x:y:z? [#permalink]
01 Jul 2014, 00:53

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