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After taking N tests, each containing 100 questions, John...

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by BTGmoderatorLU » Mon Dec 18, 2017 3:21 pm
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

The OA is D.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
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by EconomistGMATTutor » Tue Dec 19, 2017 6:13 am
Hello LUANDATO.

Let's take a look at your question.

The first time John got 70% correct answers, that is to say, $$100\cdot N\cdot70\%\ =\ 100\cdot N\cdot\frac{70}{100}=70\cdot N\ correct\ answers.$$ Now, by the other hand, $$\left(N+1\right)\cdot100\cdot72\%=\left(N+1\right)\cdot100\cdot\frac{72}{100}=72\left(N+1\right)=72N+72=\ 70N+2N+72.$$ This implies that John have to make 2N+72 correct answers to get an average equal to 72%.

This is why the correct answer is [spoiler]D=2N+72[/spoiler].

I hope this explanation may help you.

Feel free to ask me again if you have a doubt.

Regards.
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by [email protected] » Thu Dec 21, 2017 10:24 am
Hi LUANDATO,

We're told that John takes N tests, each containing 100 questions, and has an average score of 70%. We're asked for the number of correct answers John needs to score on the next test to raise his average to 72%. This question can be solved by TESTing VALUES.

IF... N=2
Then John took 2 tests and correctly answered (.7)(2)(100) = 140 questions of the 200 total questions.

With a 3rd test, John will then have answered 300 total questions. To get 72% of that overall total correct, he would need to answer (.72)(300) = 216 questions correct. He's already answered 140 questions correct, so he would need to answer 76 of the next 100 questions correctly to raise his overall average to 72%. Thus, we're looking for an answer that equals 76 when N=2. There's only one answer that matches.

Final Answer: D

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by Scott@TargetTestPrep » Mon Sep 09, 2019 6:28 pm
BTGmoderatorLU 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

The OA is D.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
Letting x = the score on his next test so that his average is 72%, we can create the equation:

(0.7 * 100N + x)/(N + 1) = 72

70N + x = 72N + 72

x = 2N + 72

Answer: D

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