ETS about VEnn diagram...pls hlp

[Anu]

In a graduating class of 236 students, 142 took algebra and 121 took chemistry. What is the greatest possible number of students that could have taken both algebra and chemistry?

 

i thought the answer is 27 but it says 121. Can you explain "by greatest possible number" .

 

any help is appreciated. Thanks

[PatentClerk]

27 is the least possible number. For highest possible common students, look at the number of chemistry students. 121 students took chemistry so if they all took algebra that would be the highest possible number.

[rabbitsfoot]

Hi Anu,

 

Think of it from the Venn Diagram approach.

Make two circles - A and B.

A will have 142 and B will have 121.

These two circles will have a common portion (generally when there is a Union between the two sets).

Now for greatest possible number of students that could have taken both algebra and chemistry will be the case when the union or the common portion of the two circles will be maximum.

This will happen when one circle lies inside of another.

Now, A can not lie inside B because A = 142 and B = 121.

So, B will lie inside of A.

In this case the union or the common portion will be the number of the persons in inner circle B which is 121.

This Union will be the answer.

[Anu]

Thanks Patent Clerk for the answer.

And Thank you Rabbits foot for clearly explaining the concept thro venn diagram. So this is how we should calculate greatest possible number ..Okay I got it. Thank you so much.

[shalin]

I think this venn diagram resource of the this venn diagram maker could resolve lot of issue.