The average (arithmetic mean) of 9 scores is \(N.\) If a 10th score is then included with the original 9, the average of

[VJesus12]

The average (arithmetic mean) of 9 scores is \(N.\) If a 10th score is then included with the original 9, the average of the 10 scores is \(T.\) Which of the following expressions represents the value of the 10th score?


(A) \(10(T−N)\)

(B) \(10T−9N\)

(C) \(\dfrac{10T−9N}{10}\)

(D) \(\dfrac{10T−9N}{9}\)

(E) \(\dfrac{10T−9N}{2}\)

[spoiler]OA=B[/spoiler]

Source: GMAT Paper Tests

[Brent@GMATPrepNow]

The average (arithmetic mean) of 9 scores is \(N.\) If a 10th score is then included with the original 9, the average of the 10 scores is \(T.\) Which of the following expressions represents the value of the 10th score?


(A) \(10(T−N)\)

(B) \(10T−9N\)

(C) \(\dfrac{10T−9N}{10}\)

(D) \(\dfrac{10T−9N}{9}\)

(E) \(\dfrac{10T−9N}{2}\)

[spoiler]OA=B[/spoiler]

Source: GMAT Paper Tests

The average (arithmetic mean) of 9 scores is N.
Let A, B, C, D, E, F, G, H, I be the original 9 scores.
So we can write: (A+B+C+D+E+F+G+H+I)/9 = N
Multiply both sides of the equation by 9 to get: A+B+C+D+E+F+G+H+I = 9N


If a 10th score is then included with the original 9, the average of the 10 scores is T
Let J be the 10th score
We can write: (A+B+C+D+E+F+G+H+I+J)/10 = T
Multiply both sides of the equation by 10 to get: A+B+C+D+E+F+G+H+I+J = 10T

Which of the following expressions represents the value of the 10th score?
In other words, which answer choice represents the value of J?

Take: A+B+C+D+E+F+G+H+I+J = 10T
In other words: A+B+C+D+E+F+G+H+I+J = 10T
Substitute to get: 9N+J = 10T
Subtract 9N from both sides of the equation to get: J = 10T - 9N

Answer: B

Cheers,
Brent

[Scott@TargetTestPrep]

The average (arithmetic mean) of 9 scores is \(N.\) If a 10th score is then included with the original 9, the average of the 10 scores is \(T.\) Which of the following expressions represents the value of the 10th score?


(A) \(10(T−N)\)

(B) \(10T−9N\)

(C) \(\dfrac{10T−9N}{10}\)

(D) \(\dfrac{10T−9N}{9}\)

(E) \(\dfrac{10T−9N}{2}\)

[spoiler]OA=B[/spoiler]

Since the sum of the first 9 scores is 9N and the sum of the 10 scores is 10T, then the 10th score must be 10T - 9N.

Answer: B