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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.

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.
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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.

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.

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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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The question in here asks for values of x:y:z and hence we require unique solution which is what we dont get from either statement (1) or statement(2) individually And even after combining, we dnt get unique solution. So ans is : E

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Guys, can you please explain how are you coming up with numerical values for the variables? Isn't this supposed to be a ratio?

1) + 2) together

y=14/x so (14z/x = 21) so 3X=2z got one relationship (ratio)

After this I cant really find anything solid for Y, there seem to be endless ways to plug variable back and forth, but I am not 100% sure that it is E.