M13-03

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

Bunuel · Accepted Answer

Official Solution:

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

Bunuel · 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

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.

amirzohrevand · Answer

I think this is a  high-quality  question and I agree with explanation.

Pakku · Answer

can you show it substituting ?

AntonioGalindo · Answer

Average = Sum / N . Where N is the number of terms

70 = Sum / N "Tests", hence Sum = 70N

72= Sum / N + 1 "Tests"

x= score required on the next test.

Substituting

72= (70N + x) / (N+1)

Solve for X

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

recusandaesaepe · Answer

I don’t quite agree with the solution. A. N−35
B. N+72
C. 2N+70
D. 2N+72
E. 2N−35

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._____

I saw the above explanation and don't agree. In this case N should be 2. N is defined as: after completing __ tests NOT "completing __ additional tests". If you complete 2 tests (initial one at 70% + one additional) and plug N=2 in, only C fits.

correct answer: C

Bunuel · Answer

That's wrong. N is the number of tests John had already taken before the next test. The next test is not included in N.

M13-03

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards