A leader needs to be selected from a group of students. If 25% of the

Question

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

A. 0.25
B. 0.3
C. 0.35
D. 0.4
E. 0.45

GMATinsight · Accepted Answer

25% of the students have leadership quality

70% of the students have good management skills

ie. Minimum Probability of (Leadership U Management skills) = 0.70
ie. Maximum Probability of (Leadership ∩ Management skills) = 1-0.70 = 0.30

ie. Maximum Probability of (Leadership U Management skills) = 0.70+0.25 = 0.95
ie. Minimum Probability of (Leadership ∩ Management skills) = 1-0.95 = 0.05

Required Difference = 0.30 - 0.05 = 0.25

Answer: Option A

KethaLikhit · Answer

hello experts
can anyone explain the solution, i couldnt understand it.
thankyou

Bunuel · Answer

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

A. 0.25
B. 0.3
C. 0.35
D. 0.4
E. 0.45

Assume there are 100 people, then 25 have leadership qualities and 70 have good management skills.

To find the maximum number of people who have neither quality, let's assume all 25 people with leadership qualities also have management skills. This means the 25-student group is a subset of the 70-student group. Therefore, the remaining 30 people do not have any of these skills.

For the minimum number, assume there is no overlap between the 25 students with leadership qualities and the 70 students with management skills. In this case, the remaining 100 - (70 + 25) = 5 students will not have any of these skills.

Therefore, the difference between the maximum and minimum probability of selecting a student who has neither of the two skills mentioned above is 30/100 - 5/100 = 25/100.

Answer: A.

A leader needs to be selected from a group of students. If 25% of the

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GMAT Problem Solving (PS) Questions

A leader needs to be selected from a group of students. If 25% of the

Prep Toolkit

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