City X has a population 4 times as great as the population of City Y,

x= 4y, y= 2*z

X : Y , Y : Z
4 : 1 , 2 : 1
8 : 2 , 2 : 1

So, X : Z = 8 : 1
(E)

A nice (fast) approach is to plug in some numbers that meet the given conditions.

City Y has a population twice as great as the population of City Z
Let's say the population of City Z is 1 person
This means the population of City Y is 2 people

City X has a population 4 times as great as the population of City Y
If the population of City Y is 2 people, then the population of City X is 8 people

So, the ratio of the population of City X to the population of City Z = 8 to 1

Answer: E

X=4Y , Y=2Z
X=4(2Z)=8Z
X/Z = 8 =>X:Z=8:1

We are given that City X has a population 4 times as great as the population of City Y and that City Y has a population twice as great as the population of City Z.

If we let the population of City X = x, the population of city Y = y, and the population of city Z = z, we can create the following equations:

x = 4y

AND

y = 2z

We need to determine the ratio of the population of City X to the population of City Z, or x/z.

To determine the ratio, we can get both x and z in terms of y, so we have:

x = 4y and z = y/2.

We can substitute 4y for x and y/2 for z in the ratio x/z:

(4y)/(y/2) = (4y)(2/y) = 8.

Thus, the ratio is 8 : 1.

Answer: E
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Make a table with xyz
TEST IT strategy
Z = 100
Y = 2Z = 200
X = 4Y = 800
X : Z = 800 : 100
8:1
E

Short and simple, start working with Z Thus, Answer must be (E) 8:1
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City X City Y. City Z

let's start from right to left : for example, let City z has 10 people

City Y has a population twice as great as the population of City Z

SO City Y has 10*2=20 people,

City X has a population 4 times as great as the population of City Y,

SO City X has 20*4= 80 people,

Q:What is the ratio of the population of City X to the population of City Z?

City X people.
___________ = 80/10 = 8/1 ( Ans E)

City Z people

Hi all,

Thank you for your answers.

If we know that
X=4Y
Y=2Z

Can't we say that X=4(2Z) so X=8Z and therefore the ratio is 1:8?

Let's pick some numbers :
X=4Y
Y=2Z => Z= 1/2Y

Let's say X= 400 so Y=100 and Z= 50

X/Z = 400/50 =800/100 = 8/1 (or you could just directly go from 400/50 = 8)

Answer E)

ScottTargetTestPrep

Hello,

I fell into this trap answer as well, but I was just following the Multipart Ratio and LCM TTP rule.
Did I make a mistake in applying it?

X:4Y and Y:2Z
1:4 and 1:2

LCM of Y = 4
x: y: z
Therefore 1: 4: 8

Please correct my logic

Hi Lucie,

You are only one step shy of the right answer.
As you found that X=8Z, now the question asks for X/Z. If X=8Z then X/Z=8/1

Let me know if you need further explanation

OH-- OMG Thank you!

Solution:

I think you are getting confused with translating the sentence "City X has a population 4 times as great as the population of City Y" into a ratio. If the population of city X is 4 times the population of city Y, then X : Y is 4 : 1, not 1 : 4. Do not confuse this ratio with the equality X = 4Y. Notice that if we divide each side of this equality by Y, we obtain X/Y = 4/1. That's why X : Y is 4 : 1.

The same idea can be applied to the ratio Y : Z; we will get that Y : Z is 2 : 1.

Now, we can use the LCM rule to express X : Y as 8 : 2, so that we get the multi-part ratio of X : Y : Z = 8 : 2 : 1. This tells us that the populations of X, Y, and Z can be represented respectively as 8k, 2k, and k for some k, and thus, the ratio of the population of city X to the population of city Y is 8k/k = 8/1, or 8 : 1.

Notice that with the correct multi-part ratio of 8 : 2 : 1, the population of city X (which is 8k) is indeed four times the population of city Y (which is 2k) and that is indeed two times the population of city Z (which is k). With the incorrect multi-part ratio of 1 : 4 : 8, we get the populations of cities X, Y and Z to be s, 4s and 8s for some s. In this case, the population of city X is actually 1/4 of the population of city Y and the population of city Y is actually 1/2 of the population of city Z. This is how one can tell the multi-part ratio of 1 : 4 : 8 is not correct.
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Answer: Option E

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