Problem Solving

Roland2rule wrote:City X has a population 4 times as great as the population of City Y, which has a population twice as great as the population of City Z. What is the ratio of the population of City X to the population of City Z?

A) 1:8
B) 1:4
C) 2:1
D) 4:1
E) 8:1

OA is e
I am confused on how to set up the formula, can any expert help me?

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

Roland2rule wrote:City X has a population 4 times as great as the population of City Y, which has a population twice as great as the population of City Z. What is the ratio of the population of City X to the population of City Z?

A) 1:8
B) 1:4
C) 2:1
D) 4:1
E) 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. We see that:

x = 4y

x = 4(2z)

z = 8z

x/z = 8

Thus, the ratio is 8 : 1.

Alternate Solution:

Let's assume that city Z has a population of 100. City Y's population, which is twice that of City Z, will then be 200. City X's population, which is 4 times as great as that of City Y, is thus 800.
So the ratio of City X's population to that of City Z is 800 : 100, or 8 : 1.

Answer: E