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In a class of 120 students, 80 enrolled for a Mathematics seminar, 60

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Bunuel
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In a class of 120 students, 80 enrolled for a Mathematics seminar, 60 [#permalink] In a class of 120 students, 80 enrolled for a Mathematics seminar, 60   05 Jun 2020, 08:08
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In a class of 120 students, 80 enrolled for a Mathematics seminar, 60 enrolled for Business Basics seminar, while 12 did not enroll for either of the 2 seminars. How many students enrolled for both the seminars?

A. 28
B. 32
C. 40
D. 48
E. 56
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BrentGMATPrepNow
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In a class of 120 students, 80 enrolled for a Mathematics seminar, 60 [#permalink] In a class of 120 students, 80 enrolled for a Mathematics seminar, 60   Updated on: 20 Sep 2020, 08:08
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In a class of 120 students, 80 enrolled for a Mathematics seminar, 60 enrolled for Business Basics seminar, while 12 did not enroll for either of the 2 seminars. How many students enrolled for both the seminars?

A. 28
B. 32
C. 40
D. 48
E. 56

One approach is to use the Double Matrix Method. This technique can be used for questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of students, and the two characteristics are:
- took Math seminar or did not take Math seminar
- took Business Basics seminar or did not take Business Basics seminar

Add all of the information to our diagram to get the following:


Answer: B

Aside: We can also use Venn diagrams or a formula to solve overlapping sets questions. However, as difficulty levels increase, it becomes harder to apply those other approaches, whereas the Double Matrix Method works every time.

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video:


EXTRA PRACTICE QUESTION

Originally posted by BrentGMATPrepNow on 05 Jun 2020, 09:02.
Last edited by BrentGMATPrepNow on 20 Sep 2020, 08:08, edited 1 time in total.
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NitishJain
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Re: In a class of 120 students, 80 enrolled for a Mathematics seminar, 60 [#permalink] In a class of 120 students, 80 enrolled for a Mathematics seminar, 60   05 Jun 2020, 08:18
IMO B

Let x be students enrolled for both

Maths =80
Both = x
Business = 60
Only Business =80-x
Neither of subjects = 12

so 80 + (60-x) + 12 = 120

152-x = 120
x =32
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Re: In a class of 120 students, 80 enrolled for a Mathematics seminar, 60 [#permalink] In a class of 120 students, 80 enrolled for a Mathematics seminar, 60   06 Jun 2020, 11:09
Given:
Total: 120,
Enrolled for Mathematics = 80,
Enrolled for Business Basics = 60
Enrolled for none = 12.

Its a venn diagram question.

Let those who enrolled only for Mathematics be a. Those who enrolled only for Business Basics be b. Those who enrolled for both be c.
=> a+b+c+12 = 120
=> Enrolled for Mathematics => a + c = 80
=> Enrolled for Business Basics => b + c = 60
Thus when we have 3 equations and 3 variables.
therefore, the value of a = 48, b = 28, c= 32.

Answer B
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Re: In a class of 120 students, 80 enrolled for a Mathematics seminar, 60 [#permalink] In a class of 120 students, 80 enrolled for a Mathematics seminar, 60   16 May 2024, 23:47
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Re: In a class of 120 students, 80 enrolled for a Mathematics seminar, 60 [#permalink]
16 May 2024, 23:47
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