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

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07 Feb 2014, 05:42
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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

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07 Feb 2014, 05:42
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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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07 Feb 2014, 12:58
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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.
##### General Discussion
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Updated on: 07 Feb 2014, 14:55
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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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Originally posted by WoundedTiger on 07 Feb 2014, 11:22.
Last edited by WoundedTiger on 07 Feb 2014, 14:55, edited 1 time in total.
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23 Apr 2014, 22:24
1
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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24 Apr 2014, 12:15
2
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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24 Apr 2014, 20:41
1
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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26 Nov 2014, 02:26
(x+y+z)/3 - (x+10+y+4+w)/3=3

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

z-w=23

D
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01 Dec 2014, 03:27
3
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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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06 Jul 2015, 07:35
2
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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16 Nov 2015, 13:08
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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.

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$$\frac{y}{3} - \frac{10+4+x}{3}=3$$
y-x=23
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17 Nov 2015, 12:53
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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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07 May 2017, 07:10
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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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03 Jan 2018, 10:22

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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29 Sep 2018, 11:04
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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:
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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30 Oct 2018, 12:08
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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01 May 2019, 13:50
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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Re: Ada and Paul received their scores on three tests. On the fi   [#permalink] 01 May 2019, 13:50
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