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Science Students - MGMAT Two Part Analysis Overlapping Sets

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Affiliations: UWC
Joined: 09 May 2012
Posts: 399
Location: India
GMAT 1: 620 Q42 V33
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Science Students - MGMAT Two Part Analysis Overlapping Sets [#permalink] New post 19 Aug 2012, 23:06
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:

[Reveal] Spoiler:
Only One Science : 33
Common to A Pair of Classes Number : 7
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Re: Science Students - MGMAT Two Part Analysis Overlapping Sets [#permalink] New post 26 Aug 2012, 00:20
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
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Re: Science Students - MGMAT Two Part Analysis Overlapping Sets [#permalink] New post 04 Oct 2012, 02:40
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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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Re: Science Students - MGMAT Two Part Analysis Overlapping Sets [#permalink] New post 26 May 2014, 05:27
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: 02 Jul 2012
Posts: 1227
Location: India
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Kudos [?]: 693 [0], given: 116

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Re: Science Students - MGMAT Two Part Analysis Overlapping Sets [#permalink] New post 26 May 2014, 07:13
Hi melaos.,

Check out the below link for clarification

advanced-overlapping-sets-problems-144260.html

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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Re: Science Students - MGMAT Two Part Analysis Overlapping Sets   [#permalink] 26 May 2014, 07:13
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