boys with an average height of \(N\) inches. What is the average height of all the students in the class?

[VJesus12]

There are \(X\) girls in a class, and their average height is \(M\) inches. In the same class, there are \(Y\) boys with an average height of \(N\) inches. What is the average height of all the students in the class?

A. \(\dfrac{X + Y}{M + N}\)

B. \(\dfrac{M + N}{X + Y}\)

C. \(\dfrac{XM + YN}{M + N}\)

D. \(\dfrac{XM + YN}{X + Y}\)

E. \(\dfrac{MN}{XY}\)

[spoiler]OA=D[/spoiler]

Source: Manhattan GMAT

[Scott@TargetTestPrep]

There are \(X\) girls in a class, and their average height is \(M\) inches. In the same class, there are \(Y\) boys with an average height of \(N\) inches. What is the average height of all the students in the class?

A. \(\dfrac{X + Y}{M + N}\)

B. \(\dfrac{M + N}{X + Y}\)

C. \(\dfrac{XM + YN}{M + N}\)

D. \(\dfrac{XM + YN}{X + Y}\)

E. \(\dfrac{MN}{XY}\)

[spoiler]OA=D[/spoiler]

Source: Manhattan GMAT

Solution:

The sum of the heights of all the girls is XM inches, and the sum of the heights of all of the boys is YN inches. The total number of students in the class is X + Y. Thus, the total height of all the X + Y students in the class is XM + YN inches. Therefore, the average height of all the students in the class is (XM + YN) / (X + Y) inches.

Answer: D