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Is there a shortcut QANT Guide 2nd Edition Q81

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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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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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by cpay3245 » Fri May 10, 2013 9:52 pm
Hi there - that is the incorrect answer according to the book....
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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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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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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
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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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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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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

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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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