What is the ratio x:y:z?

[GayaneP973]

This question comes from the FDP Strategy Guide, 5th Edition. Chapter 6, page 100, Question #9.

It is a data sufficiency question.

What is the ratio x:y:z?

(1) x+y=2z
(2) 2x+3y=z

The answer was C, both together are sufficient, neither is sufficient alone.

--
Is there a faster way of solving this question without actually manipulating the equations as suggested by the answer page?

The FDP strategy suggests the following for ratio DS questions:

1- If a Data Sufficiency question asks for the relative value of two pieces of a ratio, ANY statement that gives the relative value of ANY two pieces of the ratio will be sufficient.

2- If a DS question asks for the concrete value of one element of a ratio, you will need BOTH the concrete value of another element of the ratio AND the relative value of two elements of the ratio.

Do these tips apply to this question? If so, how? And if not, is there a general rule that we can apply to these questions that will help us reach the answer quickly?

Thank you.

[RonPurewal]

Those tips don't seem to apply to ratios involving more than two elements. (The vast majority of ratios tested will involve exactly two numbers. Ratios of three or more numbers are so rare that, most likely, the author of those tips just wasn't thinking about them at all.)

[RonPurewal]

In any case, as with just about every other GMAT quant problem, you need to formulate goals.

Here:
To get a ratio of all three elements, it's enough to get two ratios of two elements each.
In other words, if you can collect any two of the following ratios...
x:y
x:z
y:z
... then you have the ratio of all three.

(You should also be able to get from two separate ratios into a combined ratio. For instance, if I tell you that x:y is 2:3 and y:z is 4:5, you should know how to figure out that x:y:z is 8:12:15. This is irrelevant to data sufficiency, but data sufficiency is not the whole world.)

Does this make sense?

[RonPurewal]

Also, there are two things that are weird about this question (if it's presented exactly as written here):

* The case x = y = z = 0 is not excluded.
This case MUST be excluded for the ratio to have any meaning. It's impossible to define the ratio 0:0 (or 0:0:0 or whatever), just as it's impossible to define the fraction 0/0.

* Even if that case is excluded, the final ratio necessarily involves negative values.
If you double the first equation and subtract the result from the second one, you get y = -3z, implying that the ratio of y to z is -3:1.
I have NEVER seen a ratio problem from GMAC that used other than positive values.

Hmm.
I don't have the book in front of me at the moment. Is this indeed exactly the way the problem is written? If so, it needs an overhaul.

Thanks.

[BernardK777]

In the first post, GayaneP973 asked if the statement:

"If a Data Sufficiency question asks for the relative value of two pieces of a ratio, ANY statement that gives the relative value of ANY two pieces of the ratio will be sufficient." applied to the problem

This question comes from the FDP Strategy Guide, 5th Edition. Chapter 6, page 100, Question #9.

What is the ratio x:y:z?

(1) x+y=2z
(2) 2x+3y=z


Ron, you said that it doesn't seem to apply to ratios with more than 2 elements, but when solving the problem it appears to me that you did you that logic when the ratio contained three elements. So I'm confused if it in fact does work. Is there a rule that states if there are x elements, you need at least y ratios between those elements to determine the ratio between all elements. For example: if asked for the ratio of x:y:p:z how many ratios (between those elements) is sufficient to determine the full ratio?

Thanks

[tim]

As Ron mentioned, these situations are so rare that they probably weren't contemplated by the author of the rule that shows up in the book. My general advice for when you see something this rare is to use your problem solving skills to figure it out; thus your best approach to studying is to spend time developing your general problem solving skills rather than memorizing a bunch of obscure rules that will likely never be relevant on the actual GMAT.

One example of using problem solving skills is to do exactly what Ron did - simplify this down to a pair of two-variable equations from which you CAN extract ratios, according to the rule mentioned earlier. Note that Ron did not pull a ratio out of a three-variable equation as you suggest, but instead he simplified things down to a two-variable equation.

[RAHULZ400]

Hi Ron,

I got stuck regarding an approach for Question 4 ( DS question) in the Problem set of Ratios chapter. The question is as follows:

What is the ratio of x:y:z?

1) x+y = 2z
2) 2x+3y = z

Now I divided both the equations and got x/y = -3/5 hence y = -5/3x
I used this value in equation 1) and then solved as follows:

x-5x/3 = 2z

-2x/3=2z hence x/z = -1/3

so creating the table below

x y z
-3 5
-1 3

Multiplying upper values by 1 and lower by 3

x y z
-3 5
-3 9

so x:y:z = -3:5:9 which actually does not satisfy the equations and answer is 5:-3:1. Similarly if I substitute values in 2nd equation I get x/y = -3/5 and x/z = -1/3 and the final ratio becomes 3:5:9. The solution given takes ratio x/y and y/z and manages to get y = -3 for both ratios and then ratio is 5:-3:1 which is the appropriate answer. Kindly guide me what is wrong in my approach and how to solve it if I want the x term to be common numerator instead of y?

[tim]

1) x+y = 2z
2) 2x+3y = z

Now I divided both the equations and got x/y = -3/5 hence y = -5/3x

I think I see what you tried to do here, but you got the wrong result. Please go back and check your work. If you cannot find your error, please replicate each step so we can help you see where you went wrong. You made almost the exact same mistake when calculating the ratio of x to z by the way, so check your work on that one as well.

[RonPurewal]

this is the same problem as on this thread post121178.html#p121112

...so i've locked this thread.

please DO NOT DOUBLE-POST.
in general, if we see the same problem posted more than once by the same user, we'll delete ALL of those threads -- just to keep clutter off the forum.

[tim]

I'm unlocking this thread because I had already locked the other one. I'll let you ask questions on one of the threads, just not both of them!