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# A leader needs to be selected from a group of students.

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Joined: 25 Dec 2018
Posts: 146
Location: India
GMAT 1: 490 Q47 V13
GPA: 2.86
A leader needs to be selected from a group of students.  [#permalink]

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06 Jan 2019, 04:48
2
3
00:00

Difficulty:

45% (medium)

Question Stats:

68% (01:37) correct 32% (01:27) wrong based on 21 sessions

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A leader needs to be selected from a group of students. If 25% of the students have leadership quality and 70% have good management skills, what is the difference between the maximum and the minimum probability of selecting a student who has neither of the two skills mentioned above?

A 0.25
B 0.3
C 0.35
D 0.4
E 0.45
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Joined: 12 Dec 2017
Posts: 79
Location: India
Schools: Yale '19, GMBA '20, XLRI
GMAT 1: 660 Q46 V35
GPA: 3.8
Re: A leader needs to be selected from a group of students.  [#permalink]

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06 Jan 2019, 06:48
1
akurathi12 wrote:
A leader needs to be selected from a group of students. If 25% of the students have leadership quality and 70% have good management skills, what is the difference between the maximum and the minimum probability of selecting a student who has neither of the two skills mentioned above?

0.25
0.3
0.35
0.4
0.45

Lets say total students= 100
Max case = 30 students without either skills
Min case = 5 students without either skills

30-5 = 25

25/100 = 0.25
A

KUDOS IF THIS HELPS! :D
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Joined: 26 Feb 2016
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Location: India
GPA: 3.12
Re: A leader needs to be selected from a group of students.  [#permalink]

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06 Jan 2019, 07:04
1
1
akurathi12 wrote:
A leader needs to be selected from a group of students. If 25% of the students have leadership quality and 70% have good management skills, what is the difference between the maximum and the minimum probability of selecting a student who has neither of the two skills mentioned above?

A 0.25
B 0.3
C 0.35
D 0.4
E 0.45

This problem becomes easy when we assume an arbitrary number(100) for the total
number of students. 25 in a group of 100 students have leadership quality and 70 of
the total students have good management skills

Maximum probability of selecting a student who has neither of the two skills is when
all 25 students who have good leadership skills have good management skills.
Here, we have 30 students who have neither of the two skills.

Minimum probability of selecting a student who has neither of the two skills is when
all 25 students who have good leadership skills don't have good management skills.
Here, we have 5 students who have neither of the two skills.

Therefore, the difference between maximum and minimum probability is $$\frac{30-5}{100} = \frac{25}{100} =$$ 0.25(Option A)
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Re: A leader needs to be selected from a group of students.   [#permalink] 06 Jan 2019, 07:04
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