LADodgers wrote:

What is the ratio of the average (arithmetic mean) height of students in class X to the average height of students in class Y?

(1) The average height of the students in class X is 120 centimeters.

(2) The average height of the students in class X and class Y combined is 126 centimeters.

We want to find the ratio of the average height of students in class X to the average height of students in class Y. If we know the average height of students in each class, then we can find the ratio.

Statement One Alone:

The average height of the students in class X is 120 centimeters.

Without knowing the average height of the students in class Y, we can’t determine the ratio of the average height of students in class X to the average height of students in class Y.

Statement one alone is not sufficient.

Statement Two Alone:

The average height of the students in class X and class Y combined is 126 centimeters.

Even knowing that the combined (overall) average of the two classes is 126 centimeters, without knowing the average height of the students in each class, we still can’t determine the ratio of the average height of students in class X to the average height of students in class Y.

Statement two alone is not sufficient.

Statements One and Two Together:

Using statements one and two together, we can create a weighted average equation using the following:

a = the number of students in class X

120 = the average height of the students in class X

b = the number of students in class Y

y = the average height of the students in class y

126 = (120a + yb)/(a + b)

Now multiply both sides of the equation by (a + b) to get

126a + 126b = 120a + yb

6a + 126b = yb

(6a + 126b)/b = y

We need to determine the ratio of the average height of the students in class X to the average height of the students in class Y, or 120/y. Since we cannot determine a value for y, we cannot answer the question.

Answer: E

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