mgpangwi wrote:
lucieparis wrote:
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?
ScottTargetTestPrepHello,
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
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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