What is the ratio of x:y:z?

E - even with both values, there are still multiple possible solutions.

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.

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?

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?

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

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?

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.


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.

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

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?

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

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

thank you for the quick reply gmatbusters. Really helpful

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.
Answer choice: E

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?

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?


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