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Applying Alligation method for this problem

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Applying Alligation method for this problem

by Mo2men » Wed Nov 30, 2016 2:49 am
After taking N tests, each containing 100 questions, John had an average of 70% of correct answers. How much does John need to score on the next test to make his average equal 72%?

A. N−35
B. N+72
C. 2N+70
D. 2N+72
E. 2N−35

Source: GMATClub Test

I tried applying the alligation but I could not continue

Let N =1

then John has answered 70 question correctly

1 test
70.....2......72....y.....X

I could not continue to find x & y

Where did I go wrong??
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by GMATGuruNY » Wed Nov 30, 2016 5:54 am
Mo2men wrote:After taking N tests, each containing 100 questions, John had an average of 70% of correct answers. How much does John need to score on the next test to make his average equal 72%?

A. N−35
B. N+72
C. 2N+70
D. 2N+72
E. 2N−35
Let N=1, implying that John scored 70% on 1 test.
Since John will be taking a total of 2 tests, the desired average -- 72% -- must be HALFWAY between the two scores.
Since 72 is halfway between 70 and 74, the score on John's next test = 74. This is our target.

Now plug N=1 into the answers to see which yields our target of 74.
Only D works:
2N+72 = 2*1 + 72 = 74.

The correct answer is D.
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by GMATGuruNY » Wed Nov 30, 2016 6:10 am
Mo2men wrote:After taking N tests, each containing 100 questions, John had an average of 70% of correct answers. How much does John need to score on the next test to make his average equal 72%?

A. N−35
B. N+72
C. 2N+70
D. 2N+72
E. 2N−35
To learn about alligation, check here:
https://www.beatthegmat.com/ratios-fract ... 15365.html

Alligation approach for the problem above:

Let L = the last test.
Since the average score for N tests = 70%, and we want the average score for all of the tests to be 72%, we get the following number line:
N 70 ------- 72 -------- L

Let N=3.
Since there is only one additional test, L=1.
The following ratio is yielded:
N/L = 3x/x.
The distances on the number line are equal to the RECIPROCAL of this ratio:
N 70 ---x--- 72 ---3x--- L

On the resulting number line, x is the distance between 70 and 72, while 3x is the required distance between 72 and the score on the last test.
The number line implies that x = 72-70 = 2.
Thus, L = 72+3x = 72 + 3*2 = 78. This is our target.

Now plug N=3 into the answers to see which yields our target of 78.
Only D works:
2N+72 = 2*3 + 72 = 78.

The correct answer is D.
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by DavidG@VeritasPrep » Wed Nov 30, 2016 7:18 am
You could also do some good old-fashioned algebra.

Old sum = 70N
New Test = x
New Sum = 70N + x

Avg * # = Sum
72 * (N + 1) = 70N + x

Solve for x: 72N +72 = 70N + x ---> 2N + 72 = x; The answer is D
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by prada » Wed Nov 30, 2016 1:44 pm
The easiest and fastest method for me would be to chose and plug in a number. I let n=1 therefore in order for my avg to be 72% I would need a 74% on my next exam so only D gives the correct answer.
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