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Mid-way through their MBA, the students of the Class of 2012 in a busi

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Mid-way through their MBA, the students of the Class of 2012 in a busi  [#permalink]

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New post 03 Jul 2020, 02:59
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E

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Mid-way through their MBA, the students of the Class of 2012 in a business school were surveyed for career preferences. One-third of the students chose consulting as their first preference. When the survey was repeated upon completion of the MBA, it was found that two-third of the students who earlier preferred consulting had changed their mind. Among the students who chose consulting in both the surveys, three-fifths became entrepreneurs and opened consulting startups and the remaining 12 joined consulting firms as employees. How many students did the Class of 2012 have?

A. 90
B. 180
C. 210
D. 270
E. 360

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Re: Mid-way through their MBA, the students of the Class of 2012 in a busi  [#permalink]

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New post 03 Jul 2020, 03:10
1
1
Total = T

T/3 chose consulting as first preference
2/3 of T/3 changed their mind.
1/3 of T/3 still prefer consulting = T/9

3/5 of T/9 became entrepreneurs and opened consulting startups

And the remaining 12 joined consulting firms as employees. Which is 2/5 of T/9
2T/45 = 12
2T = 540
T = 270

Answer is D

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Re: Mid-way through their MBA, the students of the Class of 2012 in a busi  [#permalink]

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New post 03 Jul 2020, 03:52
Explanation:
Let students are x
Students who chooses consultancy in the first survey = x/3
Two-third changes their mind after choosing = 2/3 * x/3 =2x/9
Students chose consultancy in the second survey = x/3 - 2x/9 = x/9
Students who are entrepreneurs = 3/5
Students who stayed with their first choice = x/9 * 3/5 = x/15
Student who joined firms = 12
So,

x/9 - x/15 = 12
15x - 9x /135 = 12
6x / 135 = 12
x = 12x135/6
x = 270

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Re: Mid-way through their MBA, the students of the Class of 2012 in a busi  [#permalink]

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New post 03 Jul 2020, 04:13
Bunuel wrote:
Mid-way through their MBA, the students of the Class of 2012 in a business school were surveyed for career preferences. One-third of the students chose consulting as their first preference. When the survey was repeated upon completion of the MBA, it was found that two-third of the students who earlier preferred consulting had changed their mind. Among the students who chose consulting in both the surveys, three-fifths became entrepreneurs and opened consulting startups and the remaining 12 joined consulting firms as employees. How many students did the Class of 2012 have?

A. 90
B. 180
C. 210
D. 270
E. 360


Solution


    • Let us assume that the class of 2012 in the given business school had x students.
    • The number of students, who chose consulting as their first preference in a survey conducted mid-way of their MBA \(= x*\frac{1}{3}\)
    • When the survey was repeated upon completion of the MBA, two-third of the students who earlier preferred consulting had changed their mind.
      o This means, the number of students who chose consulting in both the surveys, \(= x*\frac{1}{3}*(1-\frac{2}{3}) = \frac{x}{9}\)
      o Among the students who chose consulting in both the surveys, three-fifths became entrepreneurs
         This means, the students who chose consulting in both the surveys and joined a consulting firm as employees \(= \frac{x}{9}*(1-\frac{3}{5})= \frac{x}{9}* \frac{2}{5} =12\)
          \( ⟹ 2x = 12*9*5\)
          \(⟹ x = 270 \)
Thus, the correct answer is Option D
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Mid-way through their MBA, the students of the Class of 2012 in a busi  [#permalink]

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New post 03 Jul 2020, 04:24
D is the answer

Total = P

1/3 P joined consulting

2/3 rd changed their mind and remaining 1/3 P * 1/3 still in consulting

3/5 of Consulting one became entrepreneurs and remaining -

2/5 * 1/9 P = 12

P = 270
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Mid-way through their MBA, the students of the Class of 2012 in a busi   [#permalink] 03 Jul 2020, 04:24

Mid-way through their MBA, the students of the Class of 2012 in a busi

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