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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]

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27 Nov 2007, 08:17
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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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27 Nov 2007, 08:23
E - even with both values, there are still multiple possible solutions.
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27 Nov 2007, 22:38
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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25 Jun 2013, 14:39
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]

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25 Jun 2013, 15:34
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]

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25 Jun 2013, 17:26
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]

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25 Jun 2013, 17:59
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]

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25 Jun 2013, 22:33
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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]

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26 Jun 2013, 13:08
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]

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26 Jun 2013, 23:29
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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]

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

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17 Dec 2015, 15:17
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Re: What is the ratio of x:y:z? [#permalink]

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19 Dec 2015, 07:57
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
Re: What is the ratio of x:y:z?   [#permalink] 19 Dec 2015, 07:57
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