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cpay3245: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Mon Apr 15, 2013 3:32 pm

by cpay3245 » Fri May 10, 2013 9:41 pm

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

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Source: Beat The GMAT — Problem Solving | Fri May 10, 2013 9:41 pm

srcc25anu: Master | Next Rank: 500 Posts; Posts: 423; Joined: Fri Jun 11, 2010 7:59 amFollowed by: 2 members; Location: Seattle, WA; Thanked: 86 times

by srcc25anu » Fri May 10, 2013 9:48 pm

Paul's score (1st / 2nd and 3rd): X --- Y --- B
Ada's score (1st / 2nd and 3rd): X+10 --- Y+4 --- A
Paul's Avg on 3 tests = (X + Y + B) / 3
Ada's Avg on 3 tests = (X + 10 + Y + 4 + A) / 3 = (X + Y + A + 14)/3
Paul's Avg GREATHER THAN Ada's Avg by 9
hence [(X + Y + B) / 3 ] - 3 = [(X + Y + A + 14)/3]
solving we get B = A + 23
hence in 3rd test, Paul must have scored 23 marks higher than Ada's score on 3rd test

Ans D

EDITED: Calculation error

Last edited by srcc25anu on Fri May 10, 2013 10:08 pm, edited 2 times in total.

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cpay3245: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Mon Apr 15, 2013 3:32 pm

by cpay3245 » Fri May 10, 2013 9:52 pm

Hi there - that is the incorrect answer according to the book....

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srcc25anu: Master | Next Rank: 500 Posts; Posts: 423; Joined: Fri Jun 11, 2010 7:59 amFollowed by: 2 members; Location: Seattle, WA; Thanked: 86 times

by srcc25anu » Fri May 10, 2013 10:09 pm

cpay3245 wrote:Hi there - that is the incorrect answer according to the book....

EDITED my post. Miscalculated 14 + 9 to be 25 instead of 23.

Ans should be D

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killerdrummer: Senior | Next Rank: 100 Posts; Posts: 89; Joined: Wed Mar 13, 2013 3:36 amFollowed by: 1 member; Thanked: 10 times

by killerdrummer » Fri May 10, 2013 10:52 pm

Let us solve this ques without using pen and paper. This process hardly takes a minute

On the first test, Ada's score was 10 points higher than Paul's score.

P's score is 10 less than A's

On the second test, Ada's score was 4 points higher than Paul's score.

P's score is now 14 less than A's

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?

P's AVERAGE ON 3 tests is 3 point higher than A's.

Means in 3rd test P has to score 9 more points than A's total so far as A IS ALREADY 14 point ahead of P.
(23-14 =9 when divided by 3 gives 3)

Hence option (d) 23

Hope that helps!

Last edited by killerdrummer on Fri May 10, 2013 10:57 pm, edited 1 time in total.

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kevincanspain: GMAT Instructor; Posts: 613; Joined: Thu Mar 22, 2007 6:17 amFollowed by: 64 members; Location: madrid; Thanked: 171 times; GMAT Score:790

by kevincanspain » Fri May 10, 2013 10:54 pm

Because Paul's average over three tests is 3 points higher than Ada's, Paul must have scored 9 points more than Ada. Over the first two tests, Ada scored 14 points more than Paul, so in the third test, Paul must have scored 23 points more than Ada

Kevin Armstrong
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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat May 11, 2013 2:02 am

cpay3245 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

Ada:
Let Ada's score on each of the 3 tests = 10.
Thus:
Ada's average = 10.

Paul:
Since Paul's average is 3 points higher than Ada's, Paul's average = 10+3 = 13.
Sum:
Since sum = number * average, the sum of Paul's 3 scores = 3*13 = 39.
First test:
Since on the first test Ada scores 10 points higher than Paul, Paul's first test = 10-10 = 0.
Second test:
Since on the second test Ada scores 4 points higher than Paul, Paul's second test = 10-4 = 6.
Thus:
Paul's third test = sum - first test - second test = 39-0-6 = 33.

Resulting difference:
Paul's third test - Ada's third test = 33-10 = 23.

The correct answer is D.

Last edited by GMATGuruNY on Wed Jun 25, 2014 8:01 am, edited 1 time in total.

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AkiB: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Sat Apr 27, 2013 5:43 am

by AkiB » Wed Jun 25, 2014 6:59 am

Since according to the question - Ada's score was 4 points higher than Paul's score

Second test:
Since on the second test Ada scores 4 points higher than Paul, Paul's second test = 10-4 = 16.

Shouldn't Paul score be 6 and not 16?

I am a little confused if someone could please help me out,

Thanks

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Jun 25, 2014 7:06 am

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

Brent Hanneson - Creator of GMATPrepNow.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Jun 25, 2014 8:03 am

AkiB wrote: Shouldn't Paul score be 6 and not 16?

Good catch.
Please see my amended post above.

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