Hi All,

When a 'weighted average' question does NOT tell you the number of entities/items involved, you can TEST VALUES to prove if there's more than one possible way to get to that average.

Here, we're asked for the ratio of the average height in Class X to the average height in Class Y. We are told NOTHING about the respective number of students in each class.

Fact 1: The average height in Class X is 120cm.

This tells us nothing about the average height in Class Y.

Fact 1 is INSUFFICIENT

Fact 2: The average height of all students in both Classes (combined) is 126cm.

IF....

Each class has 2 students in it, the average heights could be....

Class X = 126cm

Class Y = 126cm

The answer to the question is 126:126 = 1:1

Class X = 125cm

Class Y = 127cm

The answer to the question is 125:127

Fact 2 is INSUFFICIENT

Combined, we know....

The average height in Class X = 120cm

The average height of both classes = 126cm

We DON'T KNOW the number of students in each class though...

IF...

Each class has 2 students in it

The average of Class X = 120cm

The average of Class Y = 132cm

The answer to the question is 120:132

IF....

Class X has 2 students and Class Y has just 1 student

The average of Class X = 120cm

The average of Class Y = 138cm

The answer to the question is 120:138

Combined, INSUFFICIENT

Final Answer:

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Rich

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