Question

a school students at Pioneer career Kolkata wrote Mock test which has three subjects DI, VA and QA, here is the result of these

students. 80 students cleared cut off in DI, 70 in VA and 60 in QA. Only 40 students cleared all the three subjects. 10 students failed to

clear cut off even in one subjects. 50 students cleared cut off in VA and QA. 5 students cleared in cut off in only QA.

what is the minimum number of students appeared in mock test?
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Answer 1

Given:

a school students at Pioneer career Kolkata wrote Mock test which has three subjects DI, VA and QA, here is the result of these  students. 80 students cleared cut off in DI, 70 in VA and 60 in QA. Only 40 students cleared all the three subjects. 10 students failed to  clear cut off even in one subjects. 50 students cleared cut off in VA and QA. 5 students cleared in cut off in only QA.

To Find:

what is the minimum number of students who appeared in the mock test?

​Solution:

To find the solution to this question first we need to make a Venn diagram, the Venn diagram will consist of 3 sectors VA, QA, DI and a universal set. A picture has been attached of the Venn diagram

Now after filling all the areas of the Venn diagram with values. we, at last, take x as value for VA and DI and fill the remaining too

now we add up all the values to get the equation for the number of students

$N=60+20-x+x+35-x+10\\=125-x$

now to minimize the number of students we need to take x as 20

after which the number of students becomes

$for x=20\\N=125-20\\=105$

Hence, the minimum of students who appeared in the mock test is 105.