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Senior Manager  Affiliations: UWC
Joined: 09 May 2012
Posts: 359
GMAT 1: 620 Q42 V33 GMAT 2: 680 Q44 V38 GPA: 3.43
WE: Engineering (Entertainment and Sports)
Science Students - MGMAT Two Part Analysis Overlapping Sets  [#permalink]

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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, one in each column.

Only One Science___Common to A Pair of Classes_______Number
_____________ ____________________________________2
_____________ ____________________________________7
_____________ ____________________________________9
_____________ ____________________________________24
_____________ ____________________________________33
_____________ ____________________________________39

SOLUTIONS:

Only One Science : 33
Common to A Pair of Classes Number : 7
Intern  Joined: 19 Dec 2011
Posts: 13
Re: Science Students - MGMAT Two Part Analysis Overlapping Sets  [#permalink]

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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, one in each column.

Only One Science___Common to A Pair of Classes_______Number
_____________ ____________________________________2
_____________ ____________________________________7
_____________ ____________________________________9
_____________ ____________________________________24
_____________ ____________________________________33
_____________ ____________________________________39

Lets consider : Number of student studying only one science = 33.

Each class will have 11 students studying only 1 subject. 5 students study all subject. so total students studying only one and three subjects in
each class = 16.

Now we know that each class has 20 students . 20-16 = 4 will be the students in each class that should study, if selected option is correct, two
subjects. Each class has 4 students that should study two subjects and as it is evenly distributed, out of these 4 , 2 students should study one of the three subjects...

5 students will are common for all class will also be common for any two class. Therefore, 2+5 = 7.

33 , 7 is the correct answer. Check will other option it want satisfy the condition
VP  Joined: 02 Jul 2012
Posts: 1153
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42 GPA: 3.8
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Re: Science Students - MGMAT Two Part Analysis Overlapping Sets  [#permalink]

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Only in one group = x
Students common = y

x = 20 + 20 + 20 - 2(y) + 3(5)
x = 60 + 15 -2(y) = 75 - 2y

So values should satisfy the equation

x = 75 - 2y
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Intern  Joined: 09 Jan 2014
Posts: 6
Re: Science Students - MGMAT Two Part Analysis Overlapping Sets  [#permalink]

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MacFauz wrote:
Only in one group = x
Students common = y

x = 20 + 20 + 20 - 2(y) + 3(5)
x = 60 + 15 -2(y) = 75 - 2y

So values should satisfy the equation

x = 75 - 2y

don't quite understand how you get the numbers.

can pls elaborate?
VP  Joined: 02 Jul 2012
Posts: 1153
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42 GPA: 3.8
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Re: Science Students - MGMAT Two Part Analysis Overlapping Sets  [#permalink]

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Hi melaos.,

Check out the below link for clarification

melaos wrote:
MacFauz wrote:
Only in one group = x
Students common = y

x = 20 + 20 + 20 - 2(y) + 3(5)
x = 60 + 15 -2(y) = 75 - 2y

So values should satisfy the equation

x = 75 - 2y

don't quite understand how you get the numbers.

can pls elaborate?

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Joined: 15 Dec 2016
Posts: 103
Re: Science Students - MGMAT Two Part Analysis Overlapping Sets  [#permalink]

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MacFauz wrote:
Hi melaos.,

Check out the below link for clarification

melaos wrote:
MacFauz wrote:
Only in one group = x
Students common = y

x = 20 + 20 + 20 - 2(y) + 3(5)
x = 60 + 15 -2(y) = 75 - 2y

So values should satisfy the equation

x = 75 - 2y

don't quite understand how you get the numbers.

can pls elaborate?

Had a chance to look at the link -- -which formula are you using ?

Total=A+B+C−(sum of 2−group overlaps)+(all three)+NeitherTotal=A+B+C−(sum of 2−group overlaps)+(all three)+Neither.

OR

Total=A+B+C−(sum of EXACTLY 2−group overlaps)−2∗(all three)+NeitherTotal=A+B+C−(sum of EXACTLY 2−group overlaps)−2∗(all three)+Neither.
Intern  B
Joined: 15 Nov 2018
Posts: 2
Re: Science Students - MGMAT Two Part Analysis Overlapping Sets  [#permalink]

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Hi,

I don't get the same answer.

I get :
- 7 students chose one discipline only in each class
- 9 students for each pair of classes (with 4 students with 2 disciplines and 5 students with 3 disciplines) Re: Science Students - MGMAT Two Part Analysis Overlapping Sets   [#permalink] 30 Dec 2018, 12:34
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