1. ## please show the best way to solve this problem

What is the best way to solve problems like this:

If 75% of a class answered the first question on a certain test correctly, 55% answered the second question on the test correctly, and 20% answered neither of the questions correctly, what percent answered both correctly?

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2.  Reply With Quote

3. I just brake it up on the first question. 75% answered it write, 20% got it wrong and question 2 wrong, so 5% must have answered it wrong, but gotten question 2. That means that 50 of the 55% that got question two must have gotten question one as well. So 50% is your answer.  Reply With Quote

4.  Reply With Quote

5. We can solve this question using the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of students, and the two characteristics are:
- answering question #1 correctly or incorrectly
- answering question #2 correctly or incorrectly
Since the question asks us to find a PERCENT, let's say we have 100 students in TOTAL
So, we can set up our Matrix as follows: As we can see, 50 of the 100 students correctly answered BOTH questions.

Cheers,
Brent - GMAT Prep Now  Reply With Quote

6. Just.. pen down the Ven Diagram

(75-x) + (55-x) + x +20 = 100
Solve for x, x =50%. Note x = Intersection Area  Reply With Quote

7. 100-20=80............Now (75+55)-80 =50  Reply With Quote

8. I tend to use the method to map it out. The first thing you fill out is the total for Q1 right, which we know is 75, then you can fill out the total for Q2 right which is 55.
You also can fill out the Q1 wrong and Q2 wrong as 20 and the total total is 100, so it will look like this:

 Q1 right Q1 wrong Total Q2 right 55 Q2 wrong 20 Total 75 100

From there, you can figure out the total for Q2 wrong and Q1 wrong by subtracting the percentage right from the total

 Q1 right Q1 wrong Total Q2 right 55 Q2 wrong 20 45 Total 75 25 100

Then you can use the 20 wrong to figure out the rest by subtracting it from the totals and so forth

 Q1 right Q1 wrong Total Q2 right 50 5 55 Q2 wrong 25 20 45 Total 75 25 100

so you know that 50% of people answered both correctly  Reply With Quote