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

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Question Stats: 71% (02:15) correct 29% (02:27) wrong based on 1274 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

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Math Expert V
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Posts: 58402
Re: Ada and Paul received their scores on three tests. On the fi  [#permalink]

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SOLUTION

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.

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

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I solved by picking numbers.

1st exam - Ada outscores Paul by 10.

Paul - 90

2nd exam - Ada outscores Paul by 4

Paul - 90

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

Paul - 90

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.

261-194=67, therefore:

Paul - 90

Paul's score is 23 points higher. Answer D.
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Re: Ada and Paul received their scores on three tests. On the fi  [#permalink]

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

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First Test Second Test Third Test

(x+10) x (x+4) x y z

Paul 's average (arithmetic mean) score on the three tests was 3 points higher than Ada's average score on the three tests

[(x+10) + (x+4) + y ]/3 +3 = (x + x + z )/3;

= z-y =23;
Therefore Paul score on third test was 23 points greater than ada;
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Re: Ada and Paul received their scores on three tests. On the fi  [#permalink]

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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.

27 - 4 = 23.

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

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P(avg) = (T1+T2+T3)/3
P(avg) = 3
T1 = -10
T2 = -4
T3 = ?

3 = (-10 + (-4) + T3)/3

3*3 = -14 + T3
9 = -14 + T3
T3 = 23
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Re: Ada and Paul received their scores on three tests. On the fi  [#permalink]

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(x+y+z)/3 - (x+10+y+4+w)/3=3

(z-14-w)/3=3--->z-14-w=9

z-w=23

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

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1

10 ................ 0 ........... First Test

4 .................. 0 ............. Second Test

0 ................... x ............... Third Test (Say x is score by Paul in third test)

$$\frac{14}{3} + 3 = \frac{x}{3}$$

$$\frac{23}{3} = \frac{x}{3}$$

x = 23

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GMAT 1: 550 Q37 V28 GMAT 2: 610 Q43 V31 Re: Ada and Paul received their scores on three tests. On the fi  [#permalink]

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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.

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

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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

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.

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$$\frac{y}{3} - \frac{10+4+x}{3}=3$$
y-x=23
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Ada and Paul received their scores on three tests. On the fi  [#permalink]

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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 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

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

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I've approached it as follows:

1) A = P+10
2) A = P+4
3) A+x= P

(x-10-4)/3 = 3

x-14=9
x=23

not sure whether this is correct _________________
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Re: Ada and Paul received their scores on three tests. On the fi  [#permalink]

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I am getting a different answer please someone correct me

A1=P1+10
A2=P2+4

(P1+10+P2+4+P3)/3 = 3 + (A1+A2+A3)/3

(A1+A2+P3)/3 = (9+A1+A2+A3)/3
P3=9+A3
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Re: Ada and Paul received their scores on three tests. On the fi  [#permalink]

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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

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!

$$A1= P1 + 10$$
$$A2 = P2 + 4$$

$$\frac{P1 + P2 + P3}{3}= 3 + \frac{A1 + A2 + A3}{3}$$

Multiply by 3 in both sides we get
P1 + P2 + P3 = 9 + A1 + A2 + A3

P1 + P2 + P3 = 9 + P1 + 10 + P2 + 4 + A3

P1 and P2 cancel

We are interested in P3 - A3 = 9 + 10 + 4 = 23

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

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Paul was 10 points behind in 1st Test, 4 points behind in 2nd test, He has to cover up 14 points by now.
His average is 3 points higher in all test.

so he has to Cover up 10+3 in 1st Test
Cover up 4+3 in 2nd Test
and 3 points in 3rd Test. so Total is 23.
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Re: Ada and Paul received their scores on three tests. On the fi  [#permalink]

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Hi,

Here are my two cents for this question

If Paul would have scored 14 more marks than A on third test their averages would be same .

Additionally, We know that if we add or subtract each term by a constant than average will increase or decrease by that constant.

We can't add 3 to first test and we can't add 3 to second test of paul. This means we need to add 9 to third test of paul apart from scoring 14 points more than A on third test.

So 14+9=23

Was i able to explain this correctly?
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~You Just Can't beat the person who never gives up~ Babe Ruth Re: Ada and Paul received their scores on three tests. On the fi   [#permalink] 01 May 2019, 13:50
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