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# What is the ratio of x:y:z?

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Q48  V39
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Q46  V48
E - even with both values, there are still multiple possible solutions.
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lumone
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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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
lumone
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]
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]
I'm not quite sure. Perhaps someone can explain it to us. I also rewrote both proportions in terms of y.

dave785
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]
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
josemnz83
I'm not quite sure. Perhaps someone can explain it to us. I also rewrote both proportions in terms of y.

dave785
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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josemnz83
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]
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
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What is the ratio of x:y:z? [#permalink]
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.

So how can I be 100% sure here?
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Re: What is the ratio of x:y:z? [#permalink]
lumone
What is the ratio of x:y:z?

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

I think, reason behind the Correct Answer E is because the question does not specifically mention whether x,y or z is integer or not.

If it is Integer, then obviously the correct answer would have been C.

In this case, x:y:z can be 2:7:3 or 1:14:21/14 . So no unique solution.

gmatbusters : Pls correct me if I am wrong
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What is the ratio of x:y:z? [#permalink]
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yes if x, y, z had been integers, it would have been C.

But here x, y, z need not be integers, iliavko, This question can be easily understood by this
Attachment:

gc .jpg [ 120.94 KiB | Viewed 16050 times ]

merajul
lumone
What is the ratio of x:y:z?

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

I think, reason behind the Correct Answer E is because the question does not specifically mention whether x,y or z is integer or not.

If it is Integer, then obviously the correct answer would have been C.

In this case, x:y:z can be 2:7:3 or 1:14:21/14 . So unique solution.

gmatbusters : Pls correct me if I am wrong
Attachment:

gc .jpg [ 120.94 KiB | Viewed 16050 times ]
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Re: What is the ratio of x:y:z? [#permalink]
gmatbusters
yes if x, y, z had been integers, it would have been C.

But here x, y, z need not be integers, This question can be easily understood by this
Attachment:
gc%20.jpg

merajul
lumone
What is the ratio of x:y:z?

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

I think, reason behind the Correct Answer E is because the question does not specifically mention whether x,y or z is integer or not.

If it is Integer, then obviously the correct answer would have been C.

In this case, x:y:z can be 2:7:3 or 1:14:21/14 . So unique solution.

gmatbusters : Pls correct me if I am wrong
Attachment:
gc .jpg

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Re: What is the ratio of x:y:z? [#permalink]
My approach (correct me if I'm wrong):

Statement 1: xy = 14 -> Clearly not sufficient.
Statement 2: yz = 21 -> Clearly not sufficient.

Rule out A, B, D
Combining both statements:
Statement 1: y = 14/x
Statement 2: z = 21/y

Now, we can figure out:
(14/x)*z = 21
Therefore, z/x = 3/2
x:z = 2:3
y = 14/x
let's take a constant k.
x = 2k
y = 14/x = 14/2k
z = 3k

x:y:z = 2k:7/k : 3k
plug in values of k
k = 1:
x:y:z = 2:7:3

k=2:
x:y:z = 4:7/2:6 = 8:7:12

value changes. Rule out C.
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Re: What is the ratio of x:y:z? [#permalink]
Hello I had a question here GMATBusters

Why are we dividing by a variable? Aren't we supposed to not divide by variables if we don't know the sign?

GMATBusters
yes if x, y, z had been integers, it would have been C.

But here x, y, z need not be integers, iliavko, This question can be easily understood by this
Attachment:
gc%20.jpg

merajul
lumone
What is the ratio of x:y:z?

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

I think, reason behind the Correct Answer E is because the question does not specifically mention whether x,y or z is integer or not.

If it is Integer, then obviously the correct answer would have been C.

In this case, x:y:z can be 2:7:3 or 1:14:21/14 . So unique solution.

gmatbusters : Pls correct me if I am wrong
Attachment:
gc .jpg
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Re: What is the ratio of x:y:z? [#permalink]
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Hi

In equation , we can divide by a non-zero variable. Sign doesn't matter.

in case of inequality, Sign of the variable is also very important.

ax= bx
we can always divide by x (if we know it is NON-zero) to say a = b.

Example : 4 = 4
dividing by 2 gives 2=2
diving by -2 gives -2= -2

if ax>bx

if x is positive, dividing by x gives a>b

Example :-2>-4
dividing by 2 gives -1>-2

if x is negative, dividing by x gives a<b

Example :-2>-4
dividing by -2 gives 1<2

I hope it is clear .

Happy Learning

[quote="ss13ny"]Hello I had a question here GMATBusters

Why are we dividing by a variable? Aren't we supposed to not divide by variables if we don't know the sign?

Posted from my mobile device
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Re: What is the ratio of x:y:z? [#permalink]
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Re: What is the ratio of x:y:z? [#permalink]
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