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vinay1983: Legendary Member; Posts: 643; Joined: Wed Aug 14, 2013 4:27 am; Thanked: 48 times; Followed by:7 members

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by vinay1983 » Tue Sep 10, 2013 11:49 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. 0n the second test, Ada's score was 4 points higher than Paul's score. lf 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

Source: OG Quant 2nd Ed OA D

You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!

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Source: Beat The GMAT — Problem Solving | Tue Sep 10, 2013 11:49 pm

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by [email protected] » Tue Sep 10, 2013 11:57 pm

Hi vinay1983,

There are a few ways to tackle this question. You can TEST values, you can do algebra or you can work through this logically.

I'm going to show you the LOGIC approach:

We know there are 3 tests:

Test 1: Ada scores 10 more points than Paul
Test 2: Ada scores 4 more points than Paul
Test 3: Paul scores more points than Ada; enough to make his AVERAGE 3 points greater than Ada's AVERAGE.

For Paul's average to be 3 more than Ada, his TOTAL for the 3 tests needs to be 9 points higher than Ada's TOTAL.

So, he needs to "make-up" the 10 points from Test 1 + the 4 points from Test 2 + score enough points on Test 3 to put him 9 ahead of Ada.

[spoiler]10+4+9 = 23 Final Answer: D[/spoiler]

GMAT assassins aren't born, they're made,
Rich

Last edited by [email protected] on Wed Sep 11, 2013 1:34 pm, edited 1 time in total.

Contact Rich at [email protected]

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vinay1983: Legendary Member; Posts: 643; Joined: Wed Aug 14, 2013 4:27 am; Thanked: 48 times; Followed by:7 members

by vinay1983 » Wed Sep 11, 2013 12:29 am

Thanks Rich

You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!

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by Brent@GMATPrepNow » Wed Sep 11, 2013 6:53 am

vinay1983 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

Brent Hanneson - Creator of GMATPrepNow.com

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by GMATGuruNY » Wed Sep 11, 2013 8:35 am

vinay1983 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. 0n the second test, Ada's score was 4 points higher than Paul's score. lf 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

First test:
Let Paul's score = 50 and Ada's score = 60.
Second test:
Let Paul's score = 50 and Ada's score = 54.
Third test:
Let Paul's score = 50.

Since on all 3 tests Paul's score = 50, his average = 50.
Since Ada's average is 3 points lower, her average = 50-3 = 47.
Thus, Ada's sum for all 3 tests = 3*47 = 141.
Thus, Ada's score on the third test = 141-60-54 = 27.
Result:
Difference between Paul's score on the third test and Ada's score on the third test = 50-27 = 23.

The correct answer is D.

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adthedaddy: Master | Next Rank: 500 Posts; Posts: 167; Joined: Fri Mar 09, 2012 8:35 pm; Thanked: 39 times; Followed by:3 members

by adthedaddy » Wed Sep 11, 2013 8:59 am

One more simple way to solve this question can be as follows -

Let A1, A2, A3 be the scores of Ada in the tests
and P1, P2, P3 be the scores of Paul.

From the given conditions, we can form equations as -

A1 = P1 + 10
A2 = P2 + 4
A3 = P3 + C (where C is a constant we need to find)

Also, it is given that the avg score of Paul is 3 points higher than the avg score of Ada.

Thus, we can write this as -

(A1+A2+A3)/3 + 3 = (P1+P2+P3)/3

Substitute the values of A1, A2 and A3 from the given conditions, we get -

P1 + 10 + P2 + 4 + P3 + C + 9 = P1 + P2 + P3

i.e. 23 + C = 0 => C = -23

Thus, Answer = Option D

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