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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

Problem Solving Question: 81 Category:Algebra Statistics Page: 72 Difficulty: 600

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

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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

Paul 's average score on the three tests was 3 points higher than Ada's average score on the three tests, means that Paul scored 3*3 = 9 points more than Ada.

On the first two tests, Ada scored 10 + 4 = 14 points more than Paul, thus Paul's score on the third test was 9 + 14 = 23 points more than that of Ada's.

Re: Ada and Paul received their scores on three tests. On the fi [#permalink]

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07 Feb 2014, 10:22

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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?

Let Paul's score in test 1,2 and 3 be x,y and z

So Ada' score in test 1 and 2 will be x+10 ,y+4 . Let Ada's score in 3rd test be a

So as per the question (x+10+y+4+a)/3+3= (x+y+z)/3------> (x+y+14+a)/3+3= (x+y+z)/3------> (14+a)/3+3= z/3 or z = (14+a)+9 or z=a+23

Ans D

650 level is okay

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Last edited by WoundedTiger on 07 Feb 2014, 13:55, edited 1 time in total.

Re: Ada and Paul received their scores on three tests. On the fi [#permalink]

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07 Feb 2014, 11:58

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I solved by picking numbers.

1st exam - Ada outscores Paul by 10.

Paul - 90 Ada - 100

2nd exam - Ada outscores Paul by 4

Paul - 90 Ada - 94

3rd Exam - We need to figure out by how many points did Paul outscore Ada.

Paul - 90 Ada - ??

If Paul's average for the 3 exams is 90, then Ada's average must be 87. Since there are 3 exams, in order to average 87 Ada needs 261 total points (87*3). To get Ada's score for the third exam, subtract the total of her first two exams from the total points needed.

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Re: Ada and Paul received their scores on three tests. On the fi [#permalink]

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24 Apr 2014, 11:15

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For this one, I used Smart Numbers...

Ada's first two test scores = 10 + 4 (sum to 14)

Paul's first two test scores = 0 + 0 (sum to 0)

To keep the math simple, I made the average of Ada's test a multiple of 3... so her last score was a 4, giving an average of 6. For Paul to have an average 3 points higher, his average has to be 9... meaning his last score is 27.

Re: Ada and Paul received their scores on three tests. On the fi [#permalink]

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06 Jul 2015, 06:35

Bunuel wrote:

SOLUTION

Paul 's average score on the three tests was 3 points higher than Ada's average score on the three tests, means that Paul scored 3*3 = 9 points more than Ada.

On the first two tests, Ada scored 10 + 4 = 14 points more than Paul, thus Paul's score on the third test was 9 + 14 = 23 points more than that of Ada's.

Answer: D.

Bunuel you are the God of quant man! I looked at the official explanation I was like what the hell! So many variables and equations and then I look at your solution and the problem becomes so so simple!! Thanks a ton! :D
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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

Problem Solving Question: 81 Category:Algebra Statistics Page: 72 Difficulty: 600

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

\(\frac{y}{3} - \frac{10+4+x}{3}=3\) y-x=23 Answer D
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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 tests In 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) = 9

On 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