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
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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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