Bunuel wrote:
Ada and Paul received their scores on three tests. On the first test, Ada's score was 10 points higher than Paul's score. On the second test, Ada's score was 4 points higher than Paul's score. If Paul 's average (arithmetic mean) score on the three tests was 3 points higher than Ada's average score on the three tests, then Paul's score on the third test was how many points higher than Ada's score?
(A) 9
(B) 14
(C) 17
(D) 23
(E) 25
Here's a slightly different approach.
Let A, B, C = Ada's 3 test scores respectively
Let X, Y, Z = Paul's 3 test scores respectively
Paul's average score on the three tests was 3 points higher than Ada's average score on the three testsIn other words, Paul's average score - Ada's average score = 3
Or, we can write: (X+Y+Z)/3 - (A+B+C)/3 = 3
Multiply both sides by 3 to get:
(X + Y + Z) - (A + B + C) = 9On the first test, Ada's score was 10 points higher than Paul's score.We can plug in some nice numbers that satisfy this condition.
Let's say that A = 10 and X = 0
On the second test, Ada's score was 4 points higher than Paul's score.Let's say that B = 4 and Y = 0
When we plug these values into
(X + Y + Z) - (A + B + C) = 9, we get:
(0 + 0 + Z) - (10 + 4 + C) = 9
Simplify: Z - C - 14 = 9
Simplify: Z - C = 23
Since Z-C represents (Paul's 3rd test score) - (Ada's 3rd test score), we can see that the correct answer is D
Cheers,
Brent