In a group, 95% members speak English, 85% speak French, 80% speak

Question

In a group, 95% members speak English, 85% speak French, 80% speak German, and 90% speak Spanish. What is the minimum possible percentage of members in the group who speak all four languages?

A. 0
B. 10
C. 20
D. 40
E. 50

gemministorm · Accepted Answer

Assuming total - 100 members
summing percentages across 4 languages - 95 + 85 + 80 + 90 = 350 with overlap.
we need to minimize members who speak all 4 hence we distribute the language slots as evenly as possible, first ensuring everyone speaks 1, then 2, then 3 languages. Only the leftover slots must go to the 4th language.
single lang: distributing 1: to each -> 350-100 = 250
speaking 2 lang: distributing 1 more to each -> 250-100 = 150
speaking 3 lang: distributing 1 more to each -> 150-100 = 50
now each member will be speaking 3 languages
remaining 50 must add on to speak 4 languages, hence minimum possible is 50

Dereno · Answer

Total number of people = 100

English speaking members = 95

French speaking members = 85

German speaking members = 80

Spanish speaking members = 90

Sum of the values = 95+85+80+90 = 350

we need to minimise the value of all 4 members :

Let’s do it my CHOCOLATE DISTRIBUTION METHOD

We have   350 chocolates and we need to distribute it to 4 sets   I, II, III, IV, where each represent the students who study one language , 2 languages, 3 languages and ALL 4 languages respectively.

Since the   max we can allocate to a set is 100 (Which is the total members= 100%)

To minimize IV , means we need to maximise (I,II, and III).

Lets first give each student 1 chocolate = I = 100

Remaining = 350-100 = 250

Let’s give each student 1 more chocolate, so the number of students who receive two chocolates (II) is 100.

Remaining chocolates = 250-100 = 150

since, all students have received the max capacity of 2 chocolates each, and we are still left with 150 chocolates.

Let’s give each of the 100 students, again 1 chocolate each (III)

so, Remaining chocolates = 150 - 100 = 50

After distributing, each student with each 3 chocolates, we are finally left with 50 chocolates.

Since it’s a 4 set problem, already three sets ( I, II, III) are filled.

NOW, the students can receive one more chocolate. There will be  50 such students  who have received 4 chocolates.

Remaining 50 students will have each 3 chocolates.

Option E (50)

Bunuel · Answer

Experts' Global Video Explanation:

https://www.youtube.com/watch?v=6VmWqKrNGsQ

wleyes · Answer

Complement of (Complement each)
With respect to 100.

Complement of (5+15+20+10) = 50

KarishmaB · Answer

Here is a video discussing max min in 4 overlapping sets:

https://www.youtube.com/watch?v=HzggG6Jd2tU

In a group, 95% members speak English, 85% speak French, 80% speak

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In a group, 95% members speak English, 85% speak French, 80% speak

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