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by srcc25anu » Mon Apr 08, 2013 12:42 pm
Students in the tenth grade at a certain high school must take at least one science course: chemistry, physics, or biology. Each of these classes contains 20 students, and any two classes
have the same number of students in common. Five students are taking all three classes simultaneously.

Using the information given, identify a possible number of students in the tenth grade taking only one science class and the corresponding number of students common to any pair of classes.
The numbers must be consistent with each other. Make only two selections (Only One Science and Common to A Pair of Classes), one in each column.


OA: 7 and 33

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by vietmoi999 » Fri Apr 19, 2013 4:51 pm
we draw Ven digram.

let x=number of student which belong to 2 group
number of student who belong to only one group would be 20-2x-5.
we try each value of x and find the coresponding value.

that is all I know.

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by vietmoi999 » Fri May 03, 2013 8:00 pm
stuck, what to do more

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by melaos » Mon May 26, 2014 5:28 am
there's another answer on this link. ... 37528.html

but i cannot understand how he get the formula

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by Camron70 » Mon Oct 20, 2014 10:00 am
a nice post is made i like it...
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by [email protected] » Sat Jan 17, 2015 10:48 pm
Hi All,

This question has a lot of details to keep track of, but since the answers are NUMBERS, we can use them to our advantage. With a bit of logic and some notes, we can TEST THE ANSWERS and find the two values that will "fit" the given "restrictions" in the prompt.

We're told that there are 3 science classes: Chemistry, Physics and Biology. The following facts are also included:
1) Each student in school takes AT LEAST 1 science class.
2) Each class contains 20 students.
3) Take any 2 classes, and they have the SAME NUMBER of COMMON students
4) 5 students take ALL 3 classes.

We're asked to find two numbers that are consistent with each other (meaning they occur in the SAME solution) for:
A) The number of students who could take JUST 1 class
B) The number that are COMMON to any 2 classes.

Here's how we can use the answers to our advantage. Since the classes contain just 20 students each, there can't be a situation in which 24, 33 or 39 have a class in common. Thus, the answer to the second question is either 7 or 9. We can now TEST those values to see how many students take 1, 2 or 3 of the classes.

Let's start with 7. We know that the 5 students who take ALL 3 classes will be COMMON to any 2, so with 7 total who fit that description, we'd have to account for 2 more students who are COMMON to any pair of classes...

Chemistry & Physics: 2 students
Chemistry & Biology: 2 students
Physics & Biology: 2 students

So, we have the 5 students who are in ALL 3 classes and the 6 students described above (who appear in 2 classes each). So far, that gives us....

Chemistry: 5 + 2 + 2 = 9 students
Physics: 5 + 2 + 2 = 9 students
Biology: 5 + 2 + 2 = 9 students

Since each class has a TOTAL of 20 students, that means that each class has ANOTHER 11 students who take JUST that 1 CLASS.

11 + 11 + 11 = 33

These values: 7 and 33 match two of the numbers in the options, so they MUST be the respective answers to the two questions.

Final Answer: 33 and 7

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