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In a group of 68 students, each student is . . . . . .

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by M7MBA » Sat Dec 30, 2017 7:40 am
In a group of 68 students, each student is registered for at least one of three classes - History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?

A. 13
B. 10
C. 9
D. 8
E. 7

The OA is the option B.

How can I calculate the number of students? I don't know what formulas should I use. Experts, I ask for your help. Thanks in advanced.
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by [email protected] » Sat Dec 30, 2017 11:29 am
Hi MY7MBA,

We're told that in a group of 68 students, each student is registered for at least one of three classes - History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, thirty-four students are registered for English and only three students are registered for all three classes. We're asked for the number of students who are registered for EXACTLY TWO classes.

A three-group Overlapping Sets question can be solved in a coupe of ways: with a 3-circle Venn Diagram or with a Formula:

Total = (Gp. 1) + (Gp. 2) + (Gp. 3) - (Gp 1&2) - (Gp1&3) - (Gp2&3) - 2(All 3)

With the data in the prompt, we can fill in most of the formula:

Total = (Gp. 1) + (Gp. 2) + (Gp. 3) - (Gp 1&2) - (Gp1&3) - (Gp2&3) - 2(All 3)
68 = (25) + (25) + (34) - (Gp 1&2) - (Gp1&3) - (Gp2&3) - 2(3)
68 = 84 - (Gp 1&2) - (Gp1&3) - (Gp2&3) - 6
(Gp 1&2) + (Gp1&3) + (Gp2&3) = 10

While we don't know exactly how many students were in each individual "pair" of classes, we DO know that a total of 10 students were enrolled in 2 classes.

Final Answer: B

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Rich
Contact Rich at [email protected]
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by Scott@TargetTestPrep » Sun Aug 25, 2019 5:43 pm
M7MBA wrote:In a group of 68 students, each student is registered for at least one of three classes - History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?

A. 13
B. 10
C. 9
D. 8
E. 7

The OA is the option B.
We can use the following formula:

Total = # who registered for history + # who registered for math + # who registered for english - # who registered for two classes - 2(# who registered for three classes) + # who registered for no classes

Let D be the number of students who registered for exactly two classes. Then:

68 = 25 + 25 + 34 - D - 2(3) + 0

68 = 84 - D - 6 + 0

68 = 78 - D

D = 10

Answer: B

Scott Woodbury-Stewart
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[email protected]

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