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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srcc25anu
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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
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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srcc25anu
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EDITED my post. Miscalculated 14 + 9 to be 25 instead of 23.cpay3245 wrote:Hi there - that is the incorrect answer according to the book....
Ans should be D
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killerdrummer
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Let us solve this ques without using pen and paper. This process hardly takes a minute
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!
P's score is 10 less than A'sOn the first test, Ada's score was 10 points higher than Paul's score.
P's score is now 14 less than A'sOn the second test, Ada's score was 4 points higher than Paul's score.
P's AVERAGE ON 3 tests is 3 point higher 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?
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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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
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Ada: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
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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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
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
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Here's a slightly different approach.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
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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Good catch.AkiB wrote: Shouldn't Paul score be 6 and not 16?
Please see my amended post above.
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