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What is the ratio of x:y:z?

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What is the ratio of x:y:z? [#permalink] New post 27 Nov 2007, 07:17
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What is the ratio of x:y:z?

(1) xy = 14
(2) yz = 21
[Reveal] Spoiler: OA
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 [#permalink] New post 27 Nov 2007, 07:23
E - even with both values, there are still multiple possible solutions.
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Re: Ratio DS Question [#permalink] New post 27 Nov 2007, 21:38
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.
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Re: Ratio DS Question [#permalink] New post 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.
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Re: What is the ratio of x:y:z? [#permalink] New post 25 Jun 2013, 14:34
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?
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Re: What is the ratio of x:y:z? [#permalink] New post 25 Jun 2013, 16:26
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?
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Re: What is the ratio of x:y:z? [#permalink] New post 25 Jun 2013, 16:59
Hey Lumone,

The way I figured it out was to prove that there was more than 1 answer to each ratio

(1) xy = 14

One Way: x=2, y=7
Second Way: x=14, y=1

Therefore insufficient

(2) yz = 21

Same here

One Way: x=3, y=7
Second Way: x=21, y=1

insufficient again.

Now it's either C or E

One Way: x=2, y=7, z=3... This satisfies both 1 and 2
Second Way: x=14, y=1, z=21.. This also satisfies both 1 and 2

Insufficient... go with E. Hope this helps!!
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Re: What is the ratio of x:y:z? [#permalink] New post 25 Jun 2013, 21:33
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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.
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Re: What is the ratio of x:y:z? [#permalink] New post 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.
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Re: What is the ratio of x:y:z? [#permalink] New post 26 Jun 2013, 22:29
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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.

Hope this helps.
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Re: What is the ratio of x:y:z? [#permalink] New post 01 Jul 2014, 00:53
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Re: What is the ratio of x:y:z?   [#permalink] 01 Jul 2014, 00:53
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