After M Students Took a Test, There was a Total of 64% GMAT Problem Solving

Question: After M students took a test, there was a total of 64% of correct answers. If the test contains 50 questions, what is the least number of questions that the next student have to get right to bring the total of correct answers of 70%?

1. 3M + 20
2. 3M + 35
3. 4M + 15
4. 4M + 20
5. 4M + 45

Correct Answer: B

Approach Solution (1):

Denote x as the required number of the correct answers.

x must satisfy the equation: \(\frac{0.64*M*50+X}{50M+50}=\frac{7}{10}\)

OR

350M + 350 = 320M + 10x OR x = 3M + 35

Approach Solution (2):

If M tests were taken, and each test has 50 questions, then the total number of questions answered = 50 M

We are told there was a total of 64% of correct answers.

So, the total number of correctly answered questions = 64% of 50M = 32 M

If the new students take the test, then there will be M + 1 tests taken

Since each test has 50 questions, the new total number of questions answered = 50M + 50

Let C = the number of questions the new students answers correctly

So, the new number of correctly answered questions = 32M + C

We want to bring the total of correct answers to 70%

That is, we want:\(\frac{32M+C}{50M+50}=\frac{7}{100}\)

Simplify the right side: \(\frac{32M+C}{50M+50}=\frac{7}{10}\)

Multiply both sides by 10 to get:\(\frac{10(32M+C)}{50M+50}={7}\)

Multiply both sides by (50M + 50) to get: 10(32M + C) = 7(50M + 50)

Expand: 320M + 10C = 350M + 350

Subtract 320 M from both sides: 10C = 30M + 350

Divide both sides by 10 to get: C = 3M + 35

“After M students took a test, there was a total of 64% of correct answers. If the test contains 50 questions, what is the least number of questions that the next student have to get right to bring the total of correct answers of 70%?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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