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History, Math and English

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History, Math and English

by rsarashi » Sat May 27, 2017 10:43 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

OAB

Can you please explain me with the formula?
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by DavidG@VeritasPrep » Sat May 27, 2017 11:09 am
rsarashi 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

OAB

Can you please explain me with the formula?
Formula: Total = Group 1 + Group 2 + Group 3 - [# in exactly two groups] - 2[# in all three groups] + neither

If we call the # in exactly 2 groups 'x', we get:
68 = 25 + 25 + 34 - x - 2*3 + 0
68 = 78 -x
x = 10
The answer is B
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by [email protected] » Sat May 27, 2017 2:28 pm
Hi rsarashi,

3-Group Overlapping Sets questions are relatively rare on the Official GMAT (you likely will NOT see this version of Overlapping Sets on Test Day). However, there is a formula that you can use to solve it.

Total = (1st group) + (2nd group) + (3rd group) - (1st and 2nd) - (1st and 3rd) - (2nd and 3rd) - 2(all 3 groups).

In overlapping sets questions, any person who appears in more than one group has been counted more than once. When dealing with groups of people, you're not supposed to count any individual more than once, so the formula 'subtracts' all of the extra times that a person is counted.

For example, someone who is in BOTH the 1st group and the 2nd group will be counted twice....that's why we SUBTRACT that person later on [in the (1st and 2nd) group].

In this prompt, we're given the Total, a number for each of the 3 individual groups and the number of people who appear in all 3 groups. The equation would look like this...

68 = 25 + 25 + 34 - (1st and 2nd) - (1st and 3rd) - (2nd and 3rd)- 2(3)

68 = 84 - 6 - (1st and 2nd) - (1st and 3rd) - (2nd and 3rd)

68 = 78 - (1st and 2nd) - (1st and 3rd) - (2nd and 3rd)

(1st and 2nd) + (1st and 3rd) + (2nd and 3rd) = 10

Since the prompt asks for the total number of students that are in exactly 2 classes, we have our answer.

Final Answer: B

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by Scott@TargetTestPrep » Thu Jun 01, 2017 4:24 pm
rsarashi 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
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 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

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by ceilidh.erickson » Mon Jun 05, 2017 7:44 pm
Another approach to 3-part Overlapping Sets problems is to use a Venn diagrem. (But as Rich said, they're not common, so don't spend TOO much time studying these).
https://www.beatthegmat.com/overlapping- ... tml#765098
https://www.beatthegmat.com/plz-explain- ... tml#738130
https://www.beatthegmat.com/venn-diagram ... tml#723058

Please also POST YOUR SOURCES! It's a copyright violation to post intellectual property without citation. This question is from a Manhattan Prep CAT.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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