After taking N tests, each containing 100 questions

Question

After completing  N  tests, each with 100 questions, John achieved an average (arithmetic mean) of 70% correct answers. In terms of  N , how many questions must John answer correctly on the next test to increase his average to 72%?

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

M13-03.

Bunuel · Accepted Answer

Say N=1.

So, after 1 test John has 70 correct answers.
In 2 tests, so in 200 questions he needs to have 0.72*200=144 correct answers, so in the second test he must get 144-70=74 questions correctly.

Now, plug N=1 into the answer choices to see which one yields 74. Only option D fits.

Answer: D.

Bunuel · Answer

After completing  N  tests, each with 100 questions, John achieved an average (arithmetic mean) of 70% correct answers. In terms of  N , how many questions must John answer correctly on the next test to increase his average to 72%?

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

Let  x  be the number of questions John needs to answer correctly in the next test.
 
We know that John answered 70% of  100N  questions correctly, which is  0.70*100N=70N . He needs his average after  (N+1)  tests to be 72%, so:
 
 \frac{70N + x}{100(N+1)} = 0.72 
 
Solving for  x  gives us:
 
 x = 2N + 72

Answer: D

arpanpatnaik · Answer

Answer is  .

Total right answers before the final test = 70N
Total right answers after last test = 72/100 * (100*(N+1)) = 72N + 72

Hence total right answers in the last test = 72N + 72 - 70N = 2N + 72.

Regards,
A

pqhai · Answer

I. After N tests, John did 100N question, 70% correct = 70N question correct.
II. After (N + 1) tests, John did 100(N+1) question, 72% correct = 72(N + 1) 
III. However, total correct question = 70N + x.

==> connect II and III ==> 72(N + 1) = 70N + x 
==> x = 72 + 2N

C is correct.

mau5 · Answer

Just another approach :

We can safely assume that John got 70 correct answers in each of the N tests. Thus, to make this to 72 correct answers across, the new score should be such that it contributes 2 correct answers to each of the N test, and after this, is left with an exact score of 72, thus making the new average for the (N+1) tests as 72--> 2*N+72.

D.

RajKomanapalli · Answer

Let the sum of john's scores in N tests be W

so 70 =  \frac{W}{N} 
70N = W

Now if john takes another test and his avg score has to increase to 72; Also let his score in the new test be X

72 =  \frac{W + X}{N+1}

Substituting W,

72 =  \frac{70N + X}{N+1}

72N + 72 = 70N + X

Answer is D
X = 2N + 72

giovannisumano · Answer

so far, John has answered 70N question correctly
he needs an average of 72 correct answers in each of the tests, that is 72(N+1) correct answers in total

so, he needs the following number of additional correct answers: 72(N+1)-70N = 2N+72

adityasuresh · Answer

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

Stem: Each Test has 100 questions therefore n tests will have 100N questions. We can use weighted averages.
W1/W2 = A2 -Aavg/Aavg - A1
W1 = 100N
W2 = 100
A1 = 70
A2 = ?
Aavg = 72
100N/100 = A2 - 72/72 - 70
2N + 72 = A
Therefore out of 100 questions, 2N + 72/100 * 100 Must be correct
 D

adityasuresh · Answer

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

Stem: Each Test has 100 questions therefore n tests will have 100N questions. We can use weighted averages.
W1/W2 = A2 -Aavg/Aavg - A1
W1 = 100N
W2 = 100
A1 = 70
A2 = ?
Aavg = 72
100N/100 = A2 - 72/72 - 70
2N + 72 = A
Therefore out of 100 questions, 2N + 72/100 * 100 Must be correct
 D

dhruvie · Answer

Let the marks be X.

\frac{ (Current Total Correct + New Correct)}{(Number Of Tests Till Now +1) }

\frac{ (70N + X)}{(N+1) }   = 72

Solving this we get  X = 2N + 72

After taking N tests, each containing 100 questions

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