42 students took a test in school where the passing score was 70. the mean score of the 42 students taking the exam was 75.5 while the mean score of the students who passed the test was 81, and the mean score of the students who failed was 60. How many students passed the test?

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34 people passed the test

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To find out how many students passed the test, we need to examine the information given. The passing score is 70, and we know the mean (average) score for all the students who took the test, the students who passed, and the students who failed.

Let's analyze the data:

- The mean score of all 42 students who took the test is 75.5.
- The mean score of the students who passed is 81.
- The mean score of the students who failed is 60.

To solve this problem, we'll use the concept of mean and compare it with the passing score.

First, let's calculate the total score of all the students who took the test:
Total score of all students = Mean score * Number of students
Total score of all students = 75.5 * 42 = 3171

Next, let's calculate the total score of the students who passed the test:
Total score of passing students = Mean score of passing students * Number of passing students

We don't have the number of students who passed, so let's represent it as "x":

Total score of passing students = 81 * x = 81x

Also, we can calculate the total score of the students who failed the test:
Total score of failed students = Mean score of failed students * Number of failed students

Again, we don't have the number of students who failed, so let's represent it as "(42 - x)":

Total score of failed students = 60 * (42 - x) = 60(42 - x)

Since the total score of all students is equal to the sum of the total scores of the passing students and failed students, we can write the equation:

3171 = 81x + 60(42 - x)

Now, we can simplify and solve for "x".

3171 = 81x + 2520 - 60x
3171 - 2520 = 81x - 60x
651 = 21x
x = 651/21
x ≈ 31

Therefore, approximately 31 students passed the test.