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Ada and Paul received their scores on three tests. On the fi [#permalink]
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07 Feb 2014, 05:42
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The Official Guide For GMAT® Quantitative Review, 2ND EditionAda 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 ProjectEach 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!
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Re: Ada and Paul received their scores on three tests. On the fi [#permalink]
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SOLUTIONAda 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. 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 Posted from my mobile device
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Re: Ada and Paul received their scores on three tests. On the fi [#permalink]
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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 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.
261194=67, therefore:
Paul  90 Ada  67
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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23 Apr 2014, 22:24
First Test Second Test Third Test
Ada Paul Ada Paul Ada Paul (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;
= zy =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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24 Apr 2014, 12:15
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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.
27  4 = 23.
Answer is D



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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, 20:41
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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26 Nov 2014, 02:26
(x+y+z)/3  (x+10+y+4+w)/3=3
(z14w)/3=3>z14w=9
zw=23
D



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Re: Ada and Paul received their scores on three tests. On the fi [#permalink]
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01 Dec 2014, 03:27
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Ada ........... Paul 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 Answer = D
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Re: Ada and Paul received their scores on three tests. On the fi [#permalink]
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06 Jul 2015, 07:35
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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Re: Ada and Paul received their scores on three tests. On the fi [#permalink]
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16 Nov 2015, 13:08
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Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionAda 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 ProjectEach 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! \(\frac{y}{3}  \frac{10+4+x}{3}=3\) yx=23 Answer D
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Ada and Paul received their scores on three tests. On the fi [#permalink]
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17 Nov 2015, 12:53
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 ZC 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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07 May 2017, 07:10
I've approached it as follows: 1) A = P+10 2) A = P+4 3) A+x= P (x104)/3 = 3 x14=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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03 Jan 2018, 10:22
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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